From fa3fc7dc84097cd4d2ccb8df395870b8d3834012 Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Mon, 6 Feb 2023 20:21:45 +0900 Subject: [PATCH 01/19] =?UTF-8?q?=E2=9C=A8=20Add=20function=20to=20solve?= =?UTF-8?q?=20a=20cubic=20&=20quartic=20equation?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/core/math/cython/utility.pxd | 7 + raysect/core/math/cython/utility.pyx | 201 ++++++++++++++++++++++++++- 2 files changed, 207 insertions(+), 1 deletion(-) diff --git a/raysect/core/math/cython/utility.pxd b/raysect/core/math/cython/utility.pxd index dc60576b..e5eb364c 100644 --- a/raysect/core/math/cython/utility.pxd +++ b/raysect/core/math/cython/utility.pxd @@ -70,6 +70,13 @@ cdef inline double lerp(double x0, double x1, double y0, double y1, double x) no cdef bint solve_quadratic(double a, double b, double c, double *t0, double *t1) nogil +cdef bint is_zero(double v) nogil + +cdef int solve_cubic(double a, double b, double c, double d, double *t0, double *t1, double *t2) nogil + +cdef int solve_quartic(double a, double b, double c, double d, double e, + double *t0, double *t1, double *t2, double *t3) nogil + cdef bint winding2d(double[:,::1] vertices) nogil cdef bint point_inside_polygon(double[:,::1] vertices, double ptx, double pty) diff --git a/raysect/core/math/cython/utility.pyx b/raysect/core/math/cython/utility.pyx index 0cc0a134..b1b21319 100644 --- a/raysect/core/math/cython/utility.pyx +++ b/raysect/core/math/cython/utility.pyx @@ -29,11 +29,13 @@ # ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. -from libc.math cimport sqrt +from libc.math cimport sqrt, cbrt, acos, cos, M_PI cimport cython #TODO: Write unit tests! +DEF EQN_EPS = 1.0e-9 + @cython.cdivision(True) @cython.boundscheck(False) @cython.wraparound(False) @@ -420,6 +422,182 @@ cdef bint solve_quadratic(double a, double b, double c, double *t0, double *t1) t1[0] = c / q return True +cdef inline bint is_zero(double v) nogil: + return v < EQN_EPS and v > -EQN_EPS + +@cython.cdivision(True) +cdef int solve_cubic(double a, double b, double c, double d, double *t0, double *t1, double *t2) nogil: + """ + Calculates the real roots of a cubic equation. + + The a, b, c and d arguments are the four constants of the cubic equation: + + f = a.x^3 + b.x^2 + c.x + d + + The cubic equation has 1, 2 or 3 real roots, and this function will return the number of real roots. + + The values of the real roots, are returned by setting the values of the + memory locations pointed to by t0, t1, and t2. In the case of two real roots, + both t0/t1 or t1/t2 or t2/t0 will have the same value. If there is only one real root, the values + of t1 and t2 will be undefined. + + :param double a: Cubic constant. + :param double b: Cubic constant. + :param double c: Cubic constant. + :param double d: Cubic constant. + :param double t0: 1st root of the cubic. + :param double t1: 2nd root of the cubic. + :param double t2: 3rd root of the cubic. + :return: Number of real roots. + :rtype: int + """ + cdef: + int num + double p, q, sq_b, cb_p, D, cbrt_q, phi, u, sqrt_D + + # normal form: x^3 + bx^2 + cx + d = 0 + b /= a + c /= a + d /= a + + # substitute x = y - b/3 to eliminate quadric term: y^3 + 3py + 2q = 0 + sq_b = b * b + p = 1.0 / 3.0 * (c - sq_b / 3.0) + q = 0.5 * (2.0 * b * sq_b / 27.0 - b * c / 3.0 + d) + + # calculate discriminant + cb_p = p * p * p + D = cb_p + q * q + + if is_zero(D): + + # one triple solution + if is_zero(q): + t0[0] = 0 + t1[0] = 0 + t2[0] = 0 + num = 1 + + # one single and one double solution + else: + cbrt_q = cbrt(q) + t0[0] = cbrt_q + t1[0] = cbrt_q + t2[0] = -2 * cbrt_q + num = 2 + + # Trigonometric solution for three real roots + elif D < 0: + phi = 1.0 / 3.0 * acos(-q / sqrt(-cb_p)) + u = 2.0 * sqrt(-p) + + t0[0] = u * cos(phi) + t1[0] = -u * cos(phi + M_PI / 3.0) + t2[0] = -u * cos(phi - M_PI / 3.0) + + num = 3 + + # one real solution + else: + sqrt_D = sqrt(D) + t0[0] = cbrt(sqrt_D - q) - cbrt(sqrt_D + q) + num = 1 + + # resubstitute + t0[0] -= b / 3.0 + t1[0] -= b / 3.0 + t2[0] -= b / 3.0 + + return num + + +@cython.cdivision(True) +cdef int solve_quartic(double a, double b, double c, double d, double e, + double *t0, double *t1, double *t2, double *t3) nogil: + """ + Calculates the real roots of a quartic equation. + + The a, b, c, d and e arguments are the five constants of the quartic equation: + + f = a.x^4 + b.x^3 + c.x^2 + d.x + e + + The quartic equation has 0, 1, 2, 3 or 4 real roots, and this function will return the number of real roots. + + The values of the real roots, are returned by setting the values of the + memory locations pointed to by t0, t1, t2, and t3. If there is one or two real root, + the values of t2 and t3 will be undefined. If there is no real root, + all values will be undefined. + + :param double a: Qurtic constant. + :param double b: Qurtic constant. + :param double c: Qurtic constant. + :param double d: Qurtic constant. + :param double e: Qurtic constant. + :param double t0: 1st root of the quartic. + :param double t1: 2nd root of the quartic. + :param double t2: 3rd root of the quartic. + :param double t3: 4th root of the quartic. + :return: Number of real roots. + :rtype: int + """ + cdef: + double p, q, r, sq_b, v, z + int cubic_num, num = 0 + double s0, s1, s2 + + # normal form: x^4 + bx^3 + cx^2 + dx + e = 0 + b /= a + c /= a + d /= a + e /= a + + # substitute x = y - b / 4 to eliminate quadric term: y^4 + py^2 + qy + r = 0 + sq_b = b * b + p = c - 3 * sq_b / 8.0 + q = sq_b * b / 8.0 - 0.5 * b * c + d + r = -3.0 * sq_b * sq_b / 256.0 + sq_b * c / 16.0 - b * d / 4.0 + e + + if is_zero(r): + # no absolute term: y(y^3 + py + q) = 0 + t0[0] = 0 + cubic_num = solve_cubic(1, 0, p, q, t1, t2, t3) + num = 1 + cubic_num + + else: + # solve resolvent cubic + cubic_num = solve_cubic(8.0, -4.0 * p, -8.0 * r, 4.0 * p * r - q * q, &s0, &s1, &s2) + + # take the minimum one real solution + if cubic_num == 1: + z = s0 + else: + z = max(s0, s1, s2) + + # build two quadratic equation + if 2.0 * z < p: + return 0 + else: + v = sqrt(2.0 * z - p) + + # solve two quadratic equation + if solve_quadratic(1.0, v, z - 0.5 * q / v, t0, t1): + num += 2 + if solve_quadratic(1.0, -v, z + 0.5 * q / v, t2, t3): + num += 2 + else: + if solve_quadratic(1.0, -v, z + 0.5 * q / v, t0, t1): + num += 2 + else: + return 0 + + # resubstitute + t0[0] -= b / 4.0 + t1[0] -= b / 4.0 + t2[0] -= b / 4.0 + t3[0] -= b / 4.0 + + return num + @cython.boundscheck(False) @cython.wraparound(False) @@ -540,3 +718,24 @@ def _test_winding2d(p): def _point_inside_polygon(vertices, ptx, pty): """Expose cython function for testing.""" return point_inside_polygon(vertices, ptx, pty) + +def _solve_cubic(a, b, c, d): + """Expose cython function for testing.""" + t0 = 0.0 + t1 = 0.0 + t2 = 0.0 + num = 0.0 + num = solve_cubic(a, b, c, d, &t0, &t1, &t2) + + return (t0, t1, t2, num) + +def _solve_quartic(a, b, c, d, e): + """Expose cython function for testing.""" + t0 = 0.0 + t1 = 0.0 + t2 = 0.0 + t3 = 0.0 + num = 0.0 + num = solve_quartic(a, b, c, d, e, &t0, &t1, &t2, &t3) + + return (t0, t1, t2, t3, num) From e0da6c2e351e384351205c6f9a0d060d0c513442 Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Mon, 6 Feb 2023 20:22:22 +0900 Subject: [PATCH 02/19] =?UTF-8?q?=E2=9C=A8=20Add=20torus=20primitive=20fir?= =?UTF-8?q?stly?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/primitive/torus.pxd | 43 +++++ raysect/primitive/torus.pyx | 306 ++++++++++++++++++++++++++++++++++++ 2 files changed, 349 insertions(+) create mode 100644 raysect/primitive/torus.pxd create mode 100644 raysect/primitive/torus.pyx diff --git a/raysect/primitive/torus.pxd b/raysect/primitive/torus.pxd new file mode 100644 index 00000000..d3296328 --- /dev/null +++ b/raysect/primitive/torus.pxd @@ -0,0 +1,43 @@ +# cython: language_level=3 + +# Copyright (c) 2014-2021, Dr Alex Meakins, Raysect Project +# All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions are met: +# +# 1. Redistributions of source code must retain the above copyright notice, +# this list of conditions and the following disclaimer. +# +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in the +# documentation and/or other materials provided with the distribution. +# +# 3. Neither the name of the Raysect Project nor the names of its +# contributors may be used to endorse or promote products derived from +# this software without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE +# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. + +from raysect.core cimport Primitive, Point3D, Vector3D, Ray, Intersection + +cdef class Torus(Primitive): + + cdef double _mjor_radius, _minor_radius + cdef bint _further_intersection + cdef double _next_t + cdef Point3D _cached_origin + cdef Vector3D _cached_direction + cdef Ray _cached_ray + + cdef Intersection _generate_intersection(self, Ray ray, Point3D origin, Vector3D direction, double ray_distance) diff --git a/raysect/primitive/torus.pyx b/raysect/primitive/torus.pyx new file mode 100644 index 00000000..420da2f3 --- /dev/null +++ b/raysect/primitive/torus.pyx @@ -0,0 +1,306 @@ +# cython: language_level=3 + +# Copyright (c) 2014-2021, Dr Alex Meakins, Raysect Project +# All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions are met: +# +# 1. Redistributions of source code must retain the above copyright notice, +# this list of conditions and the following disclaimer. +# +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in the +# documentation and/or other materials provided with the distribution. +# +# 3. Neither the name of the Raysect Project nor the names of its +# contributors may be used to endorse or promote products derived from +# this software without specific prior written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE +# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. + + +from raysect.core cimport Material, new_intersection, BoundingBox3D, BoundingSphere3D, new_point3d, new_normal3d, Normal3D, AffineMatrix3D +from raysect.core.math.cython cimport solve_quartic, swap_double +from libc.math import atan2, cos, sin + + +# bounding box and sphere are padded by small amounts to avoid numerical accuracy issues +DEF BOX_PADDING = 1e-9 +DEF SPHERE_PADDING = 1.000000001 + +# additional ray distance to avoid re-hitting the same surface point +DEF EPSILON = 1e-9 + + +cdef class Torus(Primitive): + """ + A torus primitive. + + The torus is defined by major and minor radius. + The major radius is the distance from the center of the tube to the center of the torus. + The minor radius is the radius of the tube. + The center of the torus corresponds to the origin of the local co-ordinate system. + The axis of revolution coincides with the z-axis + + :param float major_radius: Major radius of the torus in meters (default = 1.0). + :param float minor_radius: Minor radius of the torus in meters (default = 0.5). + :param Node parent: Scene-graph parent node or None (default = None). + :param AffineMatrix3D transform: An AffineMatrix3D defining the local co-ordinate system relative to the scene-graph parent (default = identity matrix). + :param Material material: A Material object defining the torus's material (default = None). + :param str name: A string specifying a user-friendly name for the torus (default = ""). + + :ivar float mjor_radius: The major radius of the torus in meters. + :ivar float minor_radius: The minor radius of the torus in meters. + + .. code-block:: pycon + + >>> from raysect.core import translate + >>> from raysect.primitive import Torus + >>> from raysect.optical import World + >>> from raysect.optical.material import UniformSurfaceEmitter + >>> from raysect.optical.library.spectra.colours import orange + >>> + >>> world = World() + >>> + >>> torus = Torus(1.0, 0.5, parent=world, transform=translate(3, 0, 0), + material=UniformSurfaceEmitter(orange), name="orange torus") + """ + + def __init__(self, double major_radius=1.0, double minor_radius=0.5, object parent=None, + AffineMatrix3D transform=None, Material material=None, str name=None): + + super().__init__(parent, transform, material, name) + + if major_radius < minor_radius or minor_radius < 0.0: + raise ValueError("Torus minor radius cannot be less than zero and greater than major radius.") + + self._major_radius = major_radius + self._minor_radius = minor_radius + + # initialise next intersection caching and control attributes + self._further_intersection = False + self._next_t = 0.0 + self._cached_origin = None + self._cached_direction = None + self._cached_ray = None + + @property + def major_radius(self): + """ + The major radius of this torus. + + :rtype: float + """ + return self._major_radius + + @major_radius.setter + def major_radius(self, double major_radius): + + # don't do anything if the value is unchanged + if major_radius == self._major_radius: + return + + if major_radius < 0.0: + raise ValueError("Torus major radius cannot be less than zero.") + if major_radius < self._minor_radius: + raise ValueError("Torus major radius cannot be less than minor radius.") + self._major_radius = major_radius + + # the next intersection cache has been invalidated by the major radius change + self._further_intersection = False + + # any geometry caching in the root node is now invalid, inform root + self.notify_geometry_change() + + @property + def minor_radius(self): + """ + The minor radius of this torus. + + :rtype: float + """ + return self._minor_radius + + @minor_radius.setter + def minor_radius(self, double minor_radius): + + # don't do anything if the value is unchanged + if minor_radius == self._minor_radius: + return + + if minor_radius < 0.0: + raise ValueError("Torus minor radius cannot be less than zero.") + if minor_radius > self._major_radius: + raise ValueError("Torus minor radius cannot be greater than major radius.") + self._minor_radius = minor_radius + + # the next intersection cache has been invalidated by the minor radius change + self._further_intersection = False + + # any geometry caching in the root node is now invalid, inform root + self.notify_geometry_change() + + cpdef Intersection hit(self, Ray ray): + + cdef Point3D origin + cdef Vector3D direction + cdef double sq_origin, sq_r, sq_R, dot_origin_direction, f, b, c, d, e, t0, t1, t2, t3, t_closest + + # reset further intersection state + self._further_intersection = False + + # convert ray parameters to local space + origin = ray.origin.transform(self.to_local()) + direction = ray.direction.transform(self.to_local()).normalise() + + # coefficients of quartic equation + sq_origin = origin.x * origin.x + origin.y * origin.y + origin.z * origin.z + dot_origin_direction = direction.x * origin.x + direction.y * origin.y + direction.z * origin.z + sq_r = self._minor_radius * self._minor_radius + sq_R = self._major_radius * self._major_radius + f = sq_origin - (sq_r + sq_R) + + b = 4.0 * dot_origin_direction + c = 2.0 * f + 4.0 * dot_origin_direction * dot_origin_direction + 4.0 * sq_R * direction.y * direction.y + d = 4.0 * f * dot_origin_direction + 8.0 * sq_R * origin.y * direction.y + e = f * f - 4.0 * sq_R * (sq_r - origin.y * origin.y) + + # calculate intersection distances by solving the quartic equation + # ray misses if there are no real roots of the quartic + num = solve_quartic(1.0, b, c, d, e, &t0, &t1, &t2, &t3) + + if num == 0: + return None + + elif num == 1: + # test the intersection points inside the ray search range [0, max_distance] + if t0 > ray.max_distance or t0 < 0.0: + return None + else: + t_closest = t0 + return self._generate_intersection(ray, origin, direction, t_closest) + + elif num == 2: + # ensure t0 is always smaller than t1 + if t0 > t1: + swap_double(&t0, &t1) + + + + # ensure t0 is always smaller than t1 + if t0 > t1: + swap_double(&t0, &t1) + + # test the intersection points inside the ray search range [0, max_distance] + if t0 > ray.max_distance or t1 < 0.0: + return None + + if t0 >= 0.0: + t_closest = t0 + if t1 <= ray.max_distance: + self._further_intersection = True + self._cached_ray = ray + self._cached_origin = origin + self._cached_direction = direction + self._next_t = t1 + elif t1 <= ray.max_distance: + t_closest = t1 + else: + return None + + return self._generate_intersection(ray, origin, direction, t_closest) + + cpdef Intersection next_intersection(self): + + if not self._further_intersection: + return None + + # this is the 2nd and therefore last intersection + self._further_intersection = False + return self._generate_intersection(self._cached_ray, self._cached_origin, self._cached_direction, self._next_t) + + cdef Intersection _generate_intersection(self, Ray ray, Point3D origin, Vector3D direction, double ray_distance): + + cdef Point3D hit_point, tube_centre, inside_point, outside_point + cdef Normal3D normal + cdef double phi, delta_x, delta_y, delta_z + cdef bint exiting + + # point of surface intersection in local space + hit_point = new_point3d(origin.x + ray_distance * direction.x, + origin.y + ray_distance * direction.y, + origin.z + ray_distance * direction.z) + + # normal is normalised vector from torus tube centre to hit_point + phi = atan2(hit_point.y, hit_point.x) + tube_centre = new_point3d(self._major_radius * cos(phi), self._major_radius * sin(phi), 0.0) + tube_to_hit = tube_centre.vector_to(hit_point) + normal = new_normal3d(tube_to_hit.x, tube_to_hit.y, tube_to_hit.z) + normal = normal.normalise() + + # calculate points inside and outside of surface for daughter rays to + # spawn from - these points are displaced from the surface to avoid + # re-hitting the same surface + delta_x = EPSILON * normal.x + delta_y = EPSILON * normal.y + delta_z = EPSILON * normal.z + + inside_point = new_point3d(hit_point.x - delta_x, hit_point.y - delta_y, hit_point.z - delta_z) + outside_point = new_point3d(hit_point.x + delta_x, hit_point.y + delta_y, hit_point.z + delta_z) + + # is ray exiting surface + exiting = direction.dot(normal) >= 0.0 + + return new_intersection(ray, ray_distance, self, hit_point, inside_point, outside_point, + normal, exiting, self.to_local(), self.to_root()) + + cpdef bint contains(self, Point3D point) except -1: + + cdef Point3D local_point + cdef double discriminant, distance_xy, distance_sqr, sq_R, R2_r2 + + # convert world space point to local space + local_point = point.transform(self.to_local()) + + # calculate the interior discriminant + distance_xy = local_point.x * local_point.x + local_point.y * local_point.y + distance_sqr = distance_xy + local_point.z * local_point.z + sq_R = self._major_radius * self._major_radius + R2_r2 = sq_R - self._minor_radius * self._minor_radius + discriminant = distance_sqr * distance_sqr + 2.0 * distance_sqr * R2_r2 + R2_r2 * R2_r2 - 4.0 * sq_R * distance_xy + + # point is outside torus if discriminant is greater than 0 + return discriminant <= 0.0 + + cpdef BoundingBox3D bounding_box(self): + + cdef double extent + cdef Point3D origin, lower, upper + + # obtain torus origin in world space + origin = new_point3d(0, 0, 0).transform(self.to_root()) + + # calculate upper and lower corners of box + extent = self._major_radius + self._minor_radius + BOX_PADDING + lower = new_point3d(origin.x - extent, origin.y - extent, origin.z - extent) + upper = new_point3d(origin.x + extent, origin.y + extent, origin.z + extent) + + return BoundingBox3D(lower, upper) + + cpdef BoundingSphere3D bounding_sphere(self): + cdef Point3D centre = new_point3d(0, 0, 0).transform(self.to_root()) + return BoundingSphere3D(centre, (self._major_radius + self._minor_radius) * SPHERE_PADDING) + + cpdef object instance(self, object parent=None, AffineMatrix3D transform=None, Material material=None, str name=None): + return Torus(self._major_radius, self._minor_radius, parent, transform, material, name) \ No newline at end of file From ff9efcce98d6926863064d5f079d9514269e41f6 Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Tue, 7 Feb 2023 11:51:18 +0900 Subject: [PATCH 03/19] =?UTF-8?q?=E2=9C=8F=EF=B8=8F=20fix=20typo?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/primitive/torus.pxd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/raysect/primitive/torus.pxd b/raysect/primitive/torus.pxd index d3296328..5b2c7d48 100644 --- a/raysect/primitive/torus.pxd +++ b/raysect/primitive/torus.pxd @@ -33,7 +33,7 @@ from raysect.core cimport Primitive, Point3D, Vector3D, Ray, Intersection cdef class Torus(Primitive): - cdef double _mjor_radius, _minor_radius + cdef double _major_radius, _minor_radius cdef bint _further_intersection cdef double _next_t cdef Point3D _cached_origin From 3f4eff8f1f0b3071daaa3d1431dc8956320cfd62 Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Wed, 8 Feb 2023 00:01:33 +0900 Subject: [PATCH 04/19] =?UTF-8?q?=F0=9F=8E=A8=20change=20to=20use=20descar?= =?UTF-8?q?tes-euler=20methd?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/core/math/cython/utility.pxd | 18 ++- raysect/core/math/cython/utility.pyx | 170 +++++++++++++++++++++------ 2 files changed, 153 insertions(+), 35 deletions(-) diff --git a/raysect/core/math/cython/utility.pxd b/raysect/core/math/cython/utility.pxd index e5eb364c..9c7e8c52 100644 --- a/raysect/core/math/cython/utility.pxd +++ b/raysect/core/math/cython/utility.pxd @@ -31,6 +31,8 @@ cimport cython +DEF EQN_EPS = 1.0e-9 + cdef int find_index(double[::1] x, double v) nogil cdef double interpolate(double[::1] x, double[::1] y, double p) nogil @@ -58,20 +60,32 @@ cdef inline void swap_double(double *a, double *b) nogil: a[0] = b[0] b[0] = temp +cdef inline void sort_3double(double *a, double *b, double *c) nogil: + if a[0] > b[0]: + swap_double(a, b) + if b[0] > c[0]: + swap_double(b, c) + if a[0] > c[0]: + swap_double(a, c) + cdef inline void swap_int(int *a, int *b) nogil: cdef int temp temp = a[0] a[0] = b[0] b[0] = temp +cdef inline bint is_zero(double v) nogil: + return v < EQN_EPS and v > -EQN_EPS + +cdef inline void csqrt(double x, double y, double *a, double *b) nogil: + raise NotImplementedError("Not impremented yet") + @cython.cdivision(True) cdef inline double lerp(double x0, double x1, double y0, double y1, double x) nogil: return ((y1 - y0) / (x1 - x0)) * (x - x0) + y0 cdef bint solve_quadratic(double a, double b, double c, double *t0, double *t1) nogil -cdef bint is_zero(double v) nogil - cdef int solve_cubic(double a, double b, double c, double d, double *t0, double *t1, double *t2) nogil cdef int solve_quartic(double a, double b, double c, double d, double e, diff --git a/raysect/core/math/cython/utility.pyx b/raysect/core/math/cython/utility.pyx index b1b21319..c834edd1 100644 --- a/raysect/core/math/cython/utility.pyx +++ b/raysect/core/math/cython/utility.pyx @@ -34,8 +34,6 @@ cimport cython #TODO: Write unit tests! -DEF EQN_EPS = 1.0e-9 - @cython.cdivision(True) @cython.boundscheck(False) @cython.wraparound(False) @@ -422,8 +420,6 @@ cdef bint solve_quadratic(double a, double b, double c, double *t0, double *t1) t1[0] = c / q return True -cdef inline bint is_zero(double v) nogil: - return v < EQN_EPS and v > -EQN_EPS @cython.cdivision(True) cdef int solve_cubic(double a, double b, double c, double d, double *t0, double *t1, double *t2) nogil: @@ -511,11 +507,134 @@ cdef int solve_cubic(double a, double b, double c, double d, double *t0, double return num +cdef int solve_biquadratic(double a, double c, double e, double *t0, double *t1, double *t2, double *t3) nogil: + """ + Calculate the real roots of a bi quadratic equation. + + The a, c, and e arguments are the 3 constants of the biquadratic equation: + + f = a.x^4 + c.x^2 + e + + The biquadratic equation has 0, 2, or 4 real roots, and this function will return the number of real roots. + + The values of the real roots, are returned by setting the values of the + memory locations pointed to by t0, t1, t2, and t3. If there are two or four real roots, + the values of t2 and t3 will be undefined. If there is no real root, + all values will be undefined. + + :param double a: Biquadratic constant. + :param double c: Biquadratic constant. + :param double e: Biquadratic constant. + :param double t0: 1st root of the biquadratic. + :param double t1: 2nd root of the biquadratic. + :param double t2: 3rd root of the biquadratic. + :param double t3: 4th root of the biquadratic. + :return: Number of real roots. + :rtype: int + """ + cdef double s0, s1, sx0, sx1 + + # solve quadratic for x^2 + if not solve_quadratic(a, c, e, &s0, &s1): + return 0 + + # ensure s0 < s1 + if s0 > s1: + swap_double(&s0, &s1) + + # 0 <= s0 <= s1, 4 real roots + if s0 >= 0: + sx0 = sqrt(s0) + sx1 = sqrt(s1) + t0[0] = -sx1 + t1[0] = -sx0 + t2[0] = sx0 + t3[0] = sx1 + return 4 + + # s0 < 0 <= s1, 2 real roots + elif s1 >= 0: + sx1 = sqrt(s1) + t0[0] = -sx1 + t1[0] = sx1 + return 2 + + # s0 < s1 <= 0, no real root + else: + return 0 + + +cdef int _solve_depressed_quartic(double p, double q, double r, double *t0, double *t1, double *t2, double *t3) nogil: + """ + Solve depressed quartic: x^4 + p.x^2 + q.x + r + """ + cdef: + int num + double s0, s1, s2, sr, si + + if is_zero(q): + return solve_biquadratic(1.0, p, r, t0, t1, t2, t3) + + # solve resolvent cubic: t^3 - 2pt^2 + (p^2-4r)t - q^2 = 0 + num = solve_cubic(1.0, 2.0 * p, p * p - 4.0 * r, -q * q, t0, t1, t2) + + if num > 1: + # sort roots to t0 <= t1 <= t2 + sort_3double(t0, t1, t2) + + # t0 > 0 => all roots are positive because vieta's therem: t0*t1*t2 = q^2 != 0 + if t0[0] > 0: + s0 = sqrt(t0[0]) + s1 = sqrt(t1[0]) + s2 = sqrt(t2[0]) + + if q > 0: + t0[0] = 0.5 * (-s0 -s1 -s2) + t1[0] = 0.5 * (-s0 +s1 +s2) + t2[0] = 0.5 * (+s0 -s1 +s2) + t3[0] = 0.5 * (+s0 +s1 -s2) + return 4 + else: + t0[0] = 0.5 * (-s0 -s1 +s2) + t1[0] = 0.5 * (-s0 +s1 -s2) + t2[0] = 0.5 * (+s0 -s1 -s2) + t3[0] = 0.5 * (+s0 +s1 +s2) + return 4 + + # resolvent cubic solution have 1 real root + if t0[0] < 0: + t0[0] = 0.0 + + s0 = sqrt(t0[0]) + + # calculate (sr + i*si)^2 = t1[0] + i*t2[0] + # TODO + csqrt(t0[0], t1[0], &sr, &si) + + if q > 0: + t0[0] = -0.5 * s0 - sr + t0[0] = -0.5 * s0 + sr + return 2 + else: + t0[0] = 0.5 * s0 - sr + t0[0] = 0.5 * s0 + sr + return 2 + + +@cython.cdivision(True) +cdef void one_newton_step(double b, double c, double d, double e, double *x) nogil: + cdef double fx, dfx + dfx = ((4.0 * x[0] + 3 * b) * x[0] + 2.0 * d) * x[0] + e + if not is_zero(dfx): + fx = (((x[0] + b) * x[0] + c) * x[0] + d) * x[0] + e + x[0] = x[0] - fx / dfx + + @cython.cdivision(True) cdef int solve_quartic(double a, double b, double c, double d, double e, double *t0, double *t1, double *t2, double *t3) nogil: """ - Calculates the real roots of a quartic equation. + Calculates the real roots of a quartic equation with Descartes-Euler method. The a, b, c, d and e arguments are the five constants of the quartic equation: @@ -524,7 +643,7 @@ cdef int solve_quartic(double a, double b, double c, double d, double e, The quartic equation has 0, 1, 2, 3 or 4 real roots, and this function will return the number of real roots. The values of the real roots, are returned by setting the values of the - memory locations pointed to by t0, t1, t2, and t3. If there is one or two real root, + memory locations pointed to by t0, t1, t2, and t3. If there are one or two real roots, the values of t2 and t3 will be undefined. If there is no real root, all values will be undefined. @@ -541,9 +660,8 @@ cdef int solve_quartic(double a, double b, double c, double d, double e, :rtype: int """ cdef: - double p, q, r, sq_b, v, z + double p, q, r, sq_b int cubic_num, num = 0 - double s0, s1, s2 # normal form: x^4 + bx^3 + cx^2 + dx + e = 0 b /= a @@ -564,31 +682,8 @@ cdef int solve_quartic(double a, double b, double c, double d, double e, num = 1 + cubic_num else: - # solve resolvent cubic - cubic_num = solve_cubic(8.0, -4.0 * p, -8.0 * r, 4.0 * p * r - q * q, &s0, &s1, &s2) - - # take the minimum one real solution - if cubic_num == 1: - z = s0 - else: - z = max(s0, s1, s2) - - # build two quadratic equation - if 2.0 * z < p: - return 0 - else: - v = sqrt(2.0 * z - p) - - # solve two quadratic equation - if solve_quadratic(1.0, v, z - 0.5 * q / v, t0, t1): - num += 2 - if solve_quadratic(1.0, -v, z + 0.5 * q / v, t2, t3): - num += 2 - else: - if solve_quadratic(1.0, -v, z + 0.5 * q / v, t0, t1): - num += 2 - else: - return 0 + # solve depressed quartic + num = _solve_depressed_quartic(p, q, r, t0, t1, t2, t3) # resubstitute t0[0] -= b / 4.0 @@ -596,6 +691,15 @@ cdef int solve_quartic(double a, double b, double c, double d, double e, t2[0] -= b / 4.0 t3[0] -= b / 4.0 + # One newton step for each real root + if num > 0: + one_newton_step(b, c, d, e, t0) + one_newton_step(b, c, d, e, t1) + if num > 2: + one_newton_step(b, c, d, e, t2) + if num > 3: + one_newton_step(b, c, d, e, t3) + return num From b2666894bce38a8dfac0361fc5c33e24353fc4ab Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Wed, 8 Feb 2023 23:23:41 +0900 Subject: [PATCH 05/19] =?UTF-8?q?=F0=9F=8E=A8=20alter=20solvers=20for=20cu?= =?UTF-8?q?bic=20and=20quartic?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/core/math/cython/utility.pxd | 3 - raysect/core/math/cython/utility.pyx | 218 ++++++++++++++++----------- 2 files changed, 129 insertions(+), 92 deletions(-) diff --git a/raysect/core/math/cython/utility.pxd b/raysect/core/math/cython/utility.pxd index 9c7e8c52..bd5e8890 100644 --- a/raysect/core/math/cython/utility.pxd +++ b/raysect/core/math/cython/utility.pxd @@ -77,9 +77,6 @@ cdef inline void swap_int(int *a, int *b) nogil: cdef inline bint is_zero(double v) nogil: return v < EQN_EPS and v > -EQN_EPS -cdef inline void csqrt(double x, double y, double *a, double *b) nogil: - raise NotImplementedError("Not impremented yet") - @cython.cdivision(True) cdef inline double lerp(double x0, double x1, double y0, double y1, double x) nogil: return ((y1 - y0) / (x1 - x0)) * (x - x0) + y0 diff --git a/raysect/core/math/cython/utility.pyx b/raysect/core/math/cython/utility.pyx index c834edd1..90621142 100644 --- a/raysect/core/math/cython/utility.pyx +++ b/raysect/core/math/cython/utility.pyx @@ -29,7 +29,7 @@ # ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. -from libc.math cimport sqrt, cbrt, acos, cos, M_PI +from libc.math cimport sqrt, fabs, cbrt, acos, cos, M_PI cimport cython #TODO: Write unit tests! @@ -424,87 +424,75 @@ cdef bint solve_quadratic(double a, double b, double c, double *t0, double *t1) @cython.cdivision(True) cdef int solve_cubic(double a, double b, double c, double d, double *t0, double *t1, double *t2) nogil: """ - Calculates the real roots of a cubic equation. + Calculates the roots of a cubic equation. The a, b, c and d arguments are the four constants of the cubic equation: f = a.x^3 + b.x^2 + c.x + d The cubic equation has 1, 2 or 3 real roots, and this function will return the number of real roots. + The values of the roots, are returned by setting the values of the memory locations pointed to by t0, t1, and t2. + + In the case of three real roots, the roots themselves back in t0, t1 and t2. + In the case of two real roots, a pair in t0, t1, and t2 will have the same value, and the other is a different one. + In the case of one real root, t0 will be the real root, and t1 + i * t2 will a pair of coplex-conjugated roots. - The values of the real roots, are returned by setting the values of the - memory locations pointed to by t0, t1, and t2. In the case of two real roots, - both t0/t1 or t1/t2 or t2/t0 will have the same value. If there is only one real root, the values - of t1 and t2 will be undefined. + The practical algorithm is followed by https://quarticequations.com :param double a: Cubic constant. :param double b: Cubic constant. :param double c: Cubic constant. :param double d: Cubic constant. - :param double t0: 1st root of the cubic. - :param double t1: 2nd root of the cubic. - :param double t2: 3rd root of the cubic. + :param double t0: 1st real root. + :param double t1: either 2nd real root or real part of coplex-conjugated roots. + :param double t2: either 3rd real root or imaginary part of coplex-conjugated roots. :return: Number of real roots. :rtype: int """ cdef: - int num - double p, q, sq_b, cb_p, D, cbrt_q, phi, u, sqrt_D + double q, r, sq_b, cb_q, D, A, phi, u # normal form: x^3 + bx^2 + cx + d = 0 b /= a c /= a d /= a - # substitute x = y - b/3 to eliminate quadric term: y^3 + 3py + 2q = 0 + # convert depressed cubic: y^3 + 3qy - 2r = 0 sq_b = b * b - p = 1.0 / 3.0 * (c - sq_b / 3.0) - q = 0.5 * (2.0 * b * sq_b / 27.0 - b * c / 3.0 + d) + q = (3.0 * c - sq_b) / 9.0 + r = (c * b - 3.0 * d) / 6.0 - b * sq_b / 27.0 # calculate discriminant - cb_p = p * p * p - D = cb_p + q * q - - if is_zero(D): - - # one triple solution - if is_zero(q): - t0[0] = 0 - t1[0] = 0 - t2[0] = 0 - num = 1 - - # one single and one double solution + cb_q = q * q * q + D = cb_q + r * r + + # one real root and a pair of complex-conjugate roots + if D > 0: + A = cbrt(fabs(r) + sqrt(D)) + if r < 0: + t0[0] = q / A - A - b / 3.0 else: - cbrt_q = cbrt(q) - t0[0] = cbrt_q - t1[0] = cbrt_q - t2[0] = -2 * cbrt_q - num = 2 - - # Trigonometric solution for three real roots - elif D < 0: - phi = 1.0 / 3.0 * acos(-q / sqrt(-cb_p)) - u = 2.0 * sqrt(-p) - - t0[0] = u * cos(phi) - t1[0] = -u * cos(phi + M_PI / 3.0) - t2[0] = -u * cos(phi - M_PI / 3.0) + t0[0] = A - q / A - b / 3.0 + + t1[0] = -0.5 * t0[0] - b / 3.0 + t2[0] = 0.5 * sqrt(3.0) * (A + q / A) - num = 3 + return 1 - # one real solution + # Trigonometric solution for three real roots else: - sqrt_D = sqrt(D) - t0[0] = cbrt(sqrt_D - q) - cbrt(sqrt_D + q) - num = 1 + if is_zero(q): + phi = 0.0 + elif q < 0: + phi = acos(r / sqrt(-cb_q)) / 3.0 + + u = 2.0 * sqrt(-q) - # resubstitute - t0[0] -= b / 3.0 - t1[0] -= b / 3.0 - t2[0] -= b / 3.0 + t0[0] = u * cos(phi) - b / 3.0 + t1[0] = -u * cos(phi + M_PI / 3.0) - b / 3.0 + t2[0] = -u * cos(phi - M_PI / 3.0) - b / 3.0 - return num + return 3 cdef int solve_biquadratic(double a, double c, double e, double *t0, double *t1, double *t2, double *t3) nogil: @@ -570,59 +558,109 @@ cdef int _solve_depressed_quartic(double p, double q, double r, double *t0, doub """ cdef: int num - double s0, s1, s2, sr, si + double s0, sigma, A, B, sq_A, sq_B + + if q > 0: + sigma = 1.0 + else: + sigma = -1.0 + # q = 0 => x^4 + p.x^2 + r = 0 if is_zero(q): return solve_biquadratic(1.0, p, r, t0, t1, t2, t3) - # solve resolvent cubic: t^3 - 2pt^2 + (p^2-4r)t - q^2 = 0 - num = solve_cubic(1.0, 2.0 * p, p * p - 4.0 * r, -q * q, t0, t1, t2) + # solve resolvent cubic: t^3 - 2pt^2 + (p^2-4r)t + q^2 = 0 + # using Van der Waerden's method + num = solve_cubic(1.0, -2.0 * p, p * p - 4.0 * r, q * q, t0, t1, t2) if num > 1: - # sort roots to t0 <= t1 <= t2 + # sort roots to t0 < t1 < t2 sort_3double(t0, t1, t2) - # t0 > 0 => all roots are positive because vieta's therem: t0*t1*t2 = q^2 != 0 - if t0[0] > 0: - s0 = sqrt(t0[0]) - s1 = sqrt(t1[0]) - s2 = sqrt(t2[0]) - - if q > 0: - t0[0] = 0.5 * (-s0 -s1 -s2) - t1[0] = 0.5 * (-s0 +s1 +s2) - t2[0] = 0.5 * (+s0 -s1 +s2) - t3[0] = 0.5 * (+s0 +s1 -s2) + # t0 <= 0 => t1*t2 >= 0 because vieta's therem: -t0*t1*t2 = q^2 + if t0[0] <= 0: + s0 = sqrt(-t0[0]) + A = -t1[0] - t2[0] - 2.0 * sigma * sqrt(t1[0] * t2[0]) + B = -t1[0] - t2[0] + 2.0 * sigma * sqrt(t1[0] * t2[0]) + + # four real roots + if A >= 0 and B >= 0: + sq_A = sqrt(A) + sq_B = sqrt(B) + t0[0] = 0.5 * (s0 + sq_A) + t1[0] = 0.5 * (s0 - sq_A) + t2[0] = 0.5 * (-s0 + sq_B) + t3[0] = 0.5 * (-s0 - sq_B) return 4 + + # two real roots + elif A < 0 and B >= 0: + sq_B = sqrt(B) + t0[0] = 0.5 * (-s0 + sq_B) + t1[0] = 0.5 * (-s0 - sq_B) + return 2 + + # two real roots + elif A >= 0 and B < 0: + sq_A = sqrt(A) + t0[0] = 0.5 * (s0 + sq_A) + t1[0] = 0.5 * (s0 - sq_A) + return 2 + + # no real root else: - t0[0] = 0.5 * (-s0 -s1 +s2) - t1[0] = 0.5 * (-s0 +s1 -s2) - t2[0] = 0.5 * (+s0 -s1 -s2) - t3[0] = 0.5 * (+s0 +s1 +s2) + return 0 + + # if resolvent cubic solutions have only one real root t0 + else: + if t0[0] <= 0: + s0 = sqrt(-t0[0]) + A = -2.0 * t1[0] - 2.0 * sigma * sqrt(t1[0] * t1[0] + t2[0] * t2[0]) + A = -2.0 * t1[0] + 2.0 * sigma * sqrt(t1[0] * t1[0] + t2[0] * t2[0]) + + # four real roots + if A >= 0 and B >= 0: + sq_A = sqrt(A) + sq_B = sqrt(B) + t0[0] = 0.5 * (s0 + sq_A) + t1[0] = 0.5 * (s0 - sq_A) + t2[0] = 0.5 * (-s0 + sq_B) + t3[0] = 0.5 * (-s0 - sq_B) return 4 - - # resolvent cubic solution have 1 real root - if t0[0] < 0: - t0[0] = 0.0 - - s0 = sqrt(t0[0]) - # calculate (sr + i*si)^2 = t1[0] + i*t2[0] - # TODO - csqrt(t0[0], t1[0], &sr, &si) + # two real roots + elif A < 0 and B >= 0: + sq_B = sqrt(B) + t0[0] = 0.5 * (-s0 + sq_B) + t1[0] = 0.5 * (-s0 - sq_B) + return 2 + + # two real roots + elif A >= 0 and B < 0: + sq_A = sqrt(A) + t0[0] = 0.5 * (s0 + sq_A) + t1[0] = 0.5 * (s0 - sq_A) + return 2 + + # no real root + else: + return 0 - if q > 0: - t0[0] = -0.5 * s0 - sr - t0[0] = -0.5 * s0 + sr - return 2 - else: - t0[0] = 0.5 * s0 - sr - t0[0] = 0.5 * s0 + sr - return 2 + # no real root if -t0 < 0 + return 0 @cython.cdivision(True) cdef void one_newton_step(double b, double c, double d, double e, double *x) nogil: + """ + One step Newton's method for monic quartic polinomial: x^4 + b.x^3 + c.x^2 * d.x + e = 0 + + :param double b: Qurtic constant. + :param double c: Qurtic constant. + :param double d: Qurtic constant. + :param double e: Qurtic constant. + :param double x: one root of the quartic. + """ cdef double fx, dfx dfx = ((4.0 * x[0] + 3 * b) * x[0] + 2.0 * d) * x[0] + e if not is_zero(dfx): @@ -634,7 +672,7 @@ cdef void one_newton_step(double b, double c, double d, double e, double *x) nog cdef int solve_quartic(double a, double b, double c, double d, double e, double *t0, double *t1, double *t2, double *t3) nogil: """ - Calculates the real roots of a quartic equation with Descartes-Euler method. + Calculates the real roots of a quartic equation with Van der Waerden method. The a, b, c, d and e arguments are the five constants of the quartic equation: @@ -647,6 +685,8 @@ cdef int solve_quartic(double a, double b, double c, double d, double e, the values of t2 and t3 will be undefined. If there is no real root, all values will be undefined. + The practical algorithm of Van der Waerden method is followed by https://quarticequations.com + :param double a: Qurtic constant. :param double b: Qurtic constant. :param double c: Qurtic constant. @@ -678,7 +718,7 @@ cdef int solve_quartic(double a, double b, double c, double d, double e, if is_zero(r): # no absolute term: y(y^3 + py + q) = 0 t0[0] = 0 - cubic_num = solve_cubic(1, 0, p, q, t1, t2, t3) + cubic_num = solve_cubic(1.0, 0.0, p, q, t1, t2, t3) num = 1 + cubic_num else: From bd9e062dab1fe50402f42e4b5ffbb7171b48adf6 Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Thu, 9 Feb 2023 15:00:55 +0900 Subject: [PATCH 06/19] =?UTF-8?q?=F0=9F=90=9B=20fix=20bug=20code?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/core/math/cython/utility.pyx | 29 +++++++++++++++------------- 1 file changed, 16 insertions(+), 13 deletions(-) diff --git a/raysect/core/math/cython/utility.pyx b/raysect/core/math/cython/utility.pyx index 90621142..d2dadc30 100644 --- a/raysect/core/math/cython/utility.pyx +++ b/raysect/core/math/cython/utility.pyx @@ -382,10 +382,10 @@ cdef bint solve_quadratic(double a, double b, double c, double *t0, double *t1) The a, b and c arguments are the three constants of the quadratic equation: f = a.x^2 + b.x^2 + c - + If the quadratic equation has 1 or 2 real roots, this function will return True. If there are no real roots this method will return False. - + The values of the real roots, are returned by setting the values of the memory locations pointed to by t0 and t1. In the case of a single root, both t0 and t1 will have the same value. If there are not roots, the values @@ -432,7 +432,7 @@ cdef int solve_cubic(double a, double b, double c, double d, double *t0, double The cubic equation has 1, 2 or 3 real roots, and this function will return the number of real roots. The values of the roots, are returned by setting the values of the memory locations pointed to by t0, t1, and t2. - + In the case of three real roots, the roots themselves back in t0, t1 and t2. In the case of two real roots, a pair in t0, t1, and t2 will have the same value, and the other is a different one. In the case of one real root, t0 will be the real root, and t1 + i * t2 will a pair of coplex-conjugated roots. @@ -450,8 +450,8 @@ cdef int solve_cubic(double a, double b, double c, double d, double *t0, double :rtype: int """ cdef: - double q, r, sq_b, cb_q, D, A, phi, u - + double q, r, sq_b, cb_q, D, A, z0, phi, u + # normal form: x^3 + bx^2 + cx + d = 0 b /= a c /= a @@ -465,16 +465,17 @@ cdef int solve_cubic(double a, double b, double c, double d, double *t0, double # calculate discriminant cb_q = q * q * q D = cb_q + r * r - + # one real root and a pair of complex-conjugate roots if D > 0: A = cbrt(fabs(r) + sqrt(D)) if r < 0: - t0[0] = q / A - A - b / 3.0 + z0 = q / A - A else: - t0[0] = A - q / A - b / 3.0 - - t1[0] = -0.5 * t0[0] - b / 3.0 + z0 = A - q / A + + t0[0] = z0 - b / 3.0 + t1[0] = -0.5 * z0 - b / 3.0 t2[0] = 0.5 * sqrt(3.0) * (A + q / A) return 1 @@ -483,9 +484,11 @@ cdef int solve_cubic(double a, double b, double c, double d, double *t0, double else: if is_zero(q): phi = 0.0 - elif q < 0: + + # otherwise q < 0 because of D = q^3 + r^2 < 0 + else: phi = acos(r / sqrt(-cb_q)) / 3.0 - + u = 2.0 * sqrt(-q) t0[0] = u * cos(phi) - b / 3.0 @@ -616,7 +619,7 @@ cdef int _solve_depressed_quartic(double p, double q, double r, double *t0, doub if t0[0] <= 0: s0 = sqrt(-t0[0]) A = -2.0 * t1[0] - 2.0 * sigma * sqrt(t1[0] * t1[0] + t2[0] * t2[0]) - A = -2.0 * t1[0] + 2.0 * sigma * sqrt(t1[0] * t1[0] + t2[0] * t2[0]) + B = -2.0 * t1[0] + 2.0 * sigma * sqrt(t1[0] * t1[0] + t2[0] * t2[0]) # four real roots if A >= 0 and B >= 0: From b1842c6df20615f187a2260fa491f776622b2eac Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Thu, 9 Feb 2023 19:52:23 +0900 Subject: [PATCH 07/19] =?UTF-8?q?=F0=9F=8E=A8=20add=20sorting=20function?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/core/math/cython/utility.pxd | 26 ++++++++++++++++++++------ raysect/core/math/cython/utility.pyx | 2 +- 2 files changed, 21 insertions(+), 7 deletions(-) diff --git a/raysect/core/math/cython/utility.pxd b/raysect/core/math/cython/utility.pxd index bd5e8890..9f244d02 100644 --- a/raysect/core/math/cython/utility.pxd +++ b/raysect/core/math/cython/utility.pxd @@ -60,7 +60,13 @@ cdef inline void swap_double(double *a, double *b) nogil: a[0] = b[0] b[0] = temp -cdef inline void sort_3double(double *a, double *b, double *c) nogil: +cdef inline void swap_int(int *a, int *b) nogil: + cdef int temp + temp = a[0] + a[0] = b[0] + b[0] = temp + +cdef inline void sort_three_doubles(double *a, double *b, double *c) nogil: if a[0] > b[0]: swap_double(a, b) if b[0] > c[0]: @@ -68,11 +74,19 @@ cdef inline void sort_3double(double *a, double *b, double *c) nogil: if a[0] > c[0]: swap_double(a, c) -cdef inline void swap_int(int *a, int *b) nogil: - cdef int temp - temp = a[0] - a[0] = b[0] - b[0] = temp +cdef inline void sort_four_doubles(double *a, double *b, double *c, double *d) nogil: + if a[0] > b[0]: + swap_double(a, b) + if b[0] > c[0]: + swap_double(b, c) + if c[0] > d[0]: + swap_double(c, d) + if a[0] > b[0]: + swap_double(a, b) + if b[0] > c[0]: + swap_double(b, c) + if a[0] > b[0]: + swap_double(a, b) cdef inline bint is_zero(double v) nogil: return v < EQN_EPS and v > -EQN_EPS diff --git a/raysect/core/math/cython/utility.pyx b/raysect/core/math/cython/utility.pyx index d2dadc30..22d84d1b 100644 --- a/raysect/core/math/cython/utility.pyx +++ b/raysect/core/math/cython/utility.pyx @@ -578,7 +578,7 @@ cdef int _solve_depressed_quartic(double p, double q, double r, double *t0, doub if num > 1: # sort roots to t0 < t1 < t2 - sort_3double(t0, t1, t2) + sort_three_doubles(t0, t1, t2) # t0 <= 0 => t1*t2 >= 0 because vieta's therem: -t0*t1*t2 = q^2 if t0[0] <= 0: From 16ab94aa65af69c1e34e2fecd0028a896a2e9d72 Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Fri, 10 Feb 2023 00:08:13 +0900 Subject: [PATCH 08/19] =?UTF-8?q?=F0=9F=8E=A8=20add=20torus=20class=20to?= =?UTF-8?q?=20=5F=5Finit=5F=5F=20file?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/primitive/__init__.pxd | 1 + raysect/primitive/__init__.py | 1 + 2 files changed, 2 insertions(+) diff --git a/raysect/primitive/__init__.pxd b/raysect/primitive/__init__.pxd index a8d91dd8..da0c9016 100644 --- a/raysect/primitive/__init__.pxd +++ b/raysect/primitive/__init__.pxd @@ -29,6 +29,7 @@ from raysect.primitive.box cimport Box from raysect.primitive.sphere cimport Sphere +from raysect.primitive.torus cimport Torus from raysect.primitive.cylinder cimport Cylinder from raysect.primitive.csg cimport Union, Intersect, Subtract from raysect.primitive.mesh cimport Mesh diff --git a/raysect/primitive/__init__.py b/raysect/primitive/__init__.py index 26e8cf29..f9e0e738 100644 --- a/raysect/primitive/__init__.py +++ b/raysect/primitive/__init__.py @@ -28,6 +28,7 @@ # POSSIBILITY OF SUCH DAMAGE. from .box import Box +from .torus import Torus from .sphere import Sphere from .cylinder import Cylinder from .csg import Union, Intersect, Subtract From 7ff6788403c6c8f3f63e05b83cc19d0675b762da Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Fri, 10 Feb 2023 00:09:41 +0900 Subject: [PATCH 09/19] =?UTF-8?q?=F0=9F=92=A9=20=F0=9F=8E=A8=20improve=20c?= =?UTF-8?q?ode=20and=20some=20bugs=20remain?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/primitive/torus.pyx | 129 ++++++++++++++++++++++-------------- 1 file changed, 79 insertions(+), 50 deletions(-) diff --git a/raysect/primitive/torus.pyx b/raysect/primitive/torus.pyx index 420da2f3..6d15f2c2 100644 --- a/raysect/primitive/torus.pyx +++ b/raysect/primitive/torus.pyx @@ -31,8 +31,8 @@ from raysect.core cimport Material, new_intersection, BoundingBox3D, BoundingSphere3D, new_point3d, new_normal3d, Normal3D, AffineMatrix3D -from raysect.core.math.cython cimport solve_quartic, swap_double -from libc.math import atan2, cos, sin +from raysect.core.math.cython cimport solve_quartic, swap_double, sort_three_doubles, sort_four_doubles +from libc.math cimport hypot # bounding box and sphere are padded by small amounts to avoid numerical accuracy issues @@ -51,7 +51,8 @@ cdef class Torus(Primitive): The major radius is the distance from the center of the tube to the center of the torus. The minor radius is the radius of the tube. The center of the torus corresponds to the origin of the local co-ordinate system. - The axis of revolution coincides with the z-axis + The axis of revolution coincides with the z-axis, and The center of the torus tube lies + on the x-y plane. :param float major_radius: Major radius of the torus in meters (default = 1.0). :param float minor_radius: Minor radius of the torus in meters (default = 0.5). @@ -60,7 +61,7 @@ cdef class Torus(Primitive): :param Material material: A Material object defining the torus's material (default = None). :param str name: A string specifying a user-friendly name for the torus (default = ""). - :ivar float mjor_radius: The major radius of the torus in meters. + :ivar float major_radius: The major radius of the torus in meters. :ivar float minor_radius: The minor radius of the torus in meters. .. code-block:: pycon @@ -153,9 +154,12 @@ cdef class Torus(Primitive): cpdef Intersection hit(self, Ray ray): - cdef Point3D origin - cdef Vector3D direction - cdef double sq_origin, sq_r, sq_R, dot_origin_direction, f, b, c, d, e, t0, t1, t2, t3, t_closest + cdef: + Point3D origin + Vector3D direction + double sq_origin, sq_r, sq_R, dot_origin_direction, f, b, c, d, e, t_closest + double[4] t + int i # reset further intersection state self._further_intersection = False @@ -178,46 +182,62 @@ cdef class Torus(Primitive): # calculate intersection distances by solving the quartic equation # ray misses if there are no real roots of the quartic - num = solve_quartic(1.0, b, c, d, e, &t0, &t1, &t2, &t3) + num = solve_quartic(1.0, b, c, d, e, &t[0], &t[1], &t[2], &t[3]) if num == 0: return None elif num == 1: # test the intersection points inside the ray search range [0, max_distance] - if t0 > ray.max_distance or t0 < 0.0: + if t[0] > ray.max_distance or t[0] < 0.0: return None else: - t_closest = t0 - return self._generate_intersection(ray, origin, direction, t_closest) - - elif num == 2: - # ensure t0 is always smaller than t1 - if t0 > t1: - swap_double(&t0, &t1) - + t_closest = t[0] + + else: + # sorting solutions in each number of them + if num == 2: + # ensure t0 < t1 + if t[0] > t[1]: + swap_double(&t[0], &t[1]) + + # substitute the last value into undefined variables + t[2] = t[1] + t[3] = t[1] + + elif num == 3: + # ensure t0 < t1 < t2 + sort_three_doubles(&t[0], &t[1], &t[2]) + + # substitute the last value into undefined variables + t[3] = t[2] + + elif num == 4: + # ensure t0 < t1 < t2 < t3 + sort_four_doubles(&t[0], &t[1], &t[2], &t[3]) + else: + return None + # test the intersection points inside the ray search range [0, max_distance] + if t[0] > ray.max_distance or t[3] < 0.0: + return None - # ensure t0 is always smaller than t1 - if t0 > t1: - swap_double(&t0, &t1) + for i in range(num - 1): + if t[i] >= 0.0: + t_closest = t[i] + if t[i + 1] <= ray.max_distance: + self._further_intersection = True + self._cached_ray = ray + self._cached_origin = origin + self._cached_direction = direction + self._next_t = t[i + 1] - # test the intersection points inside the ray search range [0, max_distance] - if t0 > ray.max_distance or t1 < 0.0: - return None + return self._generate_intersection(ray, origin, direction, t_closest) - if t0 >= 0.0: - t_closest = t0 - if t1 <= ray.max_distance: - self._further_intersection = True - self._cached_ray = ray - self._cached_origin = origin - self._cached_direction = direction - self._next_t = t1 - elif t1 <= ray.max_distance: - t_closest = t1 - else: - return None + if t[num - 1] <= ray.max_distance: + t_closest = t[num - 1] + else: + return None return self._generate_intersection(ray, origin, direction, t_closest) @@ -226,15 +246,15 @@ cdef class Torus(Primitive): if not self._further_intersection: return None - # this is the 2nd and therefore last intersection + # this is the 2nd intersection self._further_intersection = False return self._generate_intersection(self._cached_ray, self._cached_origin, self._cached_direction, self._next_t) cdef Intersection _generate_intersection(self, Ray ray, Point3D origin, Vector3D direction, double ray_distance): - cdef Point3D hit_point, tube_centre, inside_point, outside_point + cdef Point3D hit_point, inside_point, outside_point cdef Normal3D normal - cdef double phi, delta_x, delta_y, delta_z + cdef double alpha, delta_x, delta_y, delta_z cdef bint exiting # point of surface intersection in local space @@ -243,10 +263,8 @@ cdef class Torus(Primitive): origin.z + ray_distance * direction.z) # normal is normalised vector from torus tube centre to hit_point - phi = atan2(hit_point.y, hit_point.x) - tube_centre = new_point3d(self._major_radius * cos(phi), self._major_radius * sin(phi), 0.0) - tube_to_hit = tube_centre.vector_to(hit_point) - normal = new_normal3d(tube_to_hit.x, tube_to_hit.y, tube_to_hit.z) + alpha = self._major_radius / hypot(hit_point.x, hit_point.y) + normal = new_normal3d((1.0 - alpha) * hit_point.x, (1.0 - alpha) * hit_point.y, hit_point.z) normal = normal.normalise() # calculate points inside and outside of surface for daughter rays to @@ -285,18 +303,29 @@ cdef class Torus(Primitive): cpdef BoundingBox3D bounding_box(self): - cdef double extent - cdef Point3D origin, lower, upper + cdef: + double extent + list points + Point3D point + BoundingBox3D box - # obtain torus origin in world space - origin = new_point3d(0, 0, 0).transform(self.to_root()) + box = BoundingBox3D() - # calculate upper and lower corners of box + # calculate local bounds extent = self._major_radius + self._minor_radius + BOX_PADDING - lower = new_point3d(origin.x - extent, origin.y - extent, origin.z - extent) - upper = new_point3d(origin.x + extent, origin.y + extent, origin.z + extent) + box.lower = new_point3d(-extent, -extent, -self._minor_radius - BOX_PADDING) + box.upper = new_point3d(extent, extent, self._minor_radius + BOX_PADDING) + + # obtain local space vertices + points = box.vertices() + + # convert points to world space and build an enclosing world space bounding box + # a small degree of padding is added to avoid potential numerical accuracy issues + box = BoundingBox3D() + for point in points: + box.extend(point.transform(self.to_root()), BOX_PADDING) - return BoundingBox3D(lower, upper) + return box cpdef BoundingSphere3D bounding_sphere(self): cdef Point3D centre = new_point3d(0, 0, 0).transform(self.to_root()) From efe111de1b5fe45d9546245b601dcbece2943ba6 Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Fri, 10 Feb 2023 22:27:49 +0900 Subject: [PATCH 10/19] =?UTF-8?q?=F0=9F=90=9B=20Fix=20ray-torus=20interect?= =?UTF-8?q?ion=20implementation?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/primitive/torus.pyx | 35 +++++++++++++++++++++++------------ 1 file changed, 23 insertions(+), 12 deletions(-) diff --git a/raysect/primitive/torus.pyx b/raysect/primitive/torus.pyx index 6d15f2c2..21db4652 100644 --- a/raysect/primitive/torus.pyx +++ b/raysect/primitive/torus.pyx @@ -157,32 +157,43 @@ cdef class Torus(Primitive): cdef: Point3D origin Vector3D direction - double sq_origin, sq_r, sq_R, dot_origin_direction, f, b, c, d, e, t_closest + double sq_origin_xy, sq_direction_xy, sq_origin, sq_direction + double origin_direction_xy, origin_dot_direction, sq_r, sq_R, R2_r2 + double a, b, c, d, e, t_closest double[4] t - int i + int num, i # reset further intersection state self._further_intersection = False # convert ray parameters to local space origin = ray.origin.transform(self.to_local()) - direction = ray.direction.transform(self.to_local()).normalise() + direction = ray.direction.transform(self.to_local()) + + # calculate temporary values + sq_origin_xy = origin.x * origin.x + origin.y * origin.y + sq_direction_xy = direction.x * direction.x + direction.y * direction.y + + sq_origin = sq_origin_xy + origin.z * origin.z + sq_direction = sq_direction_xy + direction.z * direction.z + + origin_direction_xy = origin.x * direction.x + origin.y * direction.y + origin_dot_direction = origin_direction_xy + origin.z * direction.z - # coefficients of quartic equation - sq_origin = origin.x * origin.x + origin.y * origin.y + origin.z * origin.z - dot_origin_direction = direction.x * origin.x + direction.y * origin.y + direction.z * origin.z sq_r = self._minor_radius * self._minor_radius sq_R = self._major_radius * self._major_radius - f = sq_origin - (sq_r + sq_R) + R2_r2 = sq_R - sq_r - b = 4.0 * dot_origin_direction - c = 2.0 * f + 4.0 * dot_origin_direction * dot_origin_direction + 4.0 * sq_R * direction.y * direction.y - d = 4.0 * f * dot_origin_direction + 8.0 * sq_R * origin.y * direction.y - e = f * f - 4.0 * sq_R * (sq_r - origin.y * origin.y) + # coefficients of quartic equation + a = sq_direction * sq_direction + b = 4.0 * sq_direction * origin_dot_direction + c = 2.0 * (2.0 * origin_dot_direction * origin_dot_direction + sq_direction * (sq_origin + R2_r2)) - 4.0 * sq_R * sq_direction_xy + d = 4.0 * origin_dot_direction * (sq_origin + R2_r2) - 8.0 * sq_R * origin_direction_xy + e = (sq_origin + R2_r2) * (sq_origin + R2_r2) - 4.0 * sq_R * sq_origin_xy # calculate intersection distances by solving the quartic equation # ray misses if there are no real roots of the quartic - num = solve_quartic(1.0, b, c, d, e, &t[0], &t[1], &t[2], &t[3]) + num = solve_quartic(a, b, c, d, e, &t[0], &t[1], &t[2], &t[3]) if num == 0: return None From 6143bdcf72ee63750e3c59b0fba2db3da17a2d3e Mon Sep 17 00:00:00 2001 From: Koyo Munechika Date: Mon, 13 Feb 2023 14:38:06 +0900 Subject: [PATCH 11/19] =?UTF-8?q?=E2=9C=A8=20add=20demo=20script=20using?= =?UTF-8?q?=20a=20torus=20primitive?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- demos/primitives/simple_torus.py | 64 ++++++++++++++++++++++++++++++++ 1 file changed, 64 insertions(+) create mode 100644 demos/primitives/simple_torus.py diff --git a/demos/primitives/simple_torus.py b/demos/primitives/simple_torus.py new file mode 100644 index 00000000..4081283b --- /dev/null +++ b/demos/primitives/simple_torus.py @@ -0,0 +1,64 @@ +from matplotlib import pyplot as plt + +from raysect.optical import ConstantSF, Point3D, World, d65_white, rotate, translate +from raysect.optical.library.metal import Copper +from raysect.optical.material import Lambert, UniformSurfaceEmitter +from raysect.optical.observer import PinholeCamera, RGBAdaptiveSampler2D, RGBPipeline2D +from raysect.primitive import Box, Cylinder, Torus + +world = World() + +# Torus +torus = Torus( + 1.0, + 0.5, + world, + transform=translate(0, 0.0, 0.6), + material=Copper(), +) + +# floor +Box( + Point3D(-100, -100, -10), + Point3D(100, 100, 0), + parent=world, + material=Lambert(ConstantSF(1.0)), +) + +# emitter +Cylinder( + 3.0, + 100.0, + parent=world, + transform=translate(0, 0, 8) * rotate(90, 0, 0) * translate(0, 0, -50), + material=UniformSurfaceEmitter(d65_white, 1.0), +) + +# camera +rgb = RGBPipeline2D(display_unsaturated_fraction=0.995) +sampler = RGBAdaptiveSampler2D(rgb, min_samples=500, fraction=0.1, cutoff=0.01) +camera = PinholeCamera( + (512, 512), + parent=world, + transform=rotate(0, 45, 0) * translate(0, 0, 5) * rotate(0, -180, 0), + pipelines=[rgb], + frame_sampler=sampler, +) +camera.spectral_bins = 21 +camera.spectral_rays = 21 +camera.pixel_samples = 250 +camera.ray_max_depth = 10000 +camera.ray_extinction_min_depth = 3 +camera.ray_extinction_prob = 0.01 + + +# start ray tracing +plt.ion() +for p in range(0, 1000): + print(f"Rendering pass {p}...") + camera.observe() + print() + +plt.ioff() +rgb.display() +plt.show() From 3019130a433ea9b4c1be59cdcaa69ca21d86079f Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Mon, 18 Dec 2023 23:09:12 +0900 Subject: [PATCH 12/19] =?UTF-8?q?=F0=9F=A9=B9=20fix=20spectral=20rays=20in?= =?UTF-8?q?=20camera=20settings?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- demos/primitives/simple_torus.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demos/primitives/simple_torus.py b/demos/primitives/simple_torus.py index 4081283b..91c0d66e 100644 --- a/demos/primitives/simple_torus.py +++ b/demos/primitives/simple_torus.py @@ -45,7 +45,7 @@ frame_sampler=sampler, ) camera.spectral_bins = 21 -camera.spectral_rays = 21 +camera.spectral_rays = 1 camera.pixel_samples = 250 camera.ray_max_depth = 10000 camera.ray_extinction_min_depth = 3 From 893c4eb4db8f429a959b494bb0037bea9a2934c6 Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Mon, 18 Dec 2023 23:10:44 +0900 Subject: [PATCH 13/19] =?UTF-8?q?=F0=9F=8E=A8=20=E2=9C=8F=EF=B8=8F=20Fix?= =?UTF-8?q?=20formatting=20and=20typos=20in=20utility.pyx=20and=20torus.py?= =?UTF-8?q?x?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/core/math/cython/utility.pyx | 23 +++++++++++++---------- raysect/primitive/torus.pyx | 13 ++++++------- 2 files changed, 19 insertions(+), 17 deletions(-) diff --git a/raysect/core/math/cython/utility.pyx b/raysect/core/math/cython/utility.pyx index 22d84d1b..f5fa3e19 100644 --- a/raysect/core/math/cython/utility.pyx +++ b/raysect/core/math/cython/utility.pyx @@ -389,9 +389,9 @@ cdef bint solve_quadratic(double a, double b, double c, double *t0, double *t1) The values of the real roots, are returned by setting the values of the memory locations pointed to by t0 and t1. In the case of a single root, both t0 and t1 will have the same value. If there are not roots, the values - of t0 and t1 will be undefined. + of t0 and t1 will be undefined. - :param double a: Quadratic constant. + :param double a: Quadratic constant. :param double b: Quadratic constant. :param double c: Quadratic constant. :param double t0: 1st root of the quadratic. @@ -430,16 +430,19 @@ cdef int solve_cubic(double a, double b, double c, double d, double *t0, double f = a.x^3 + b.x^2 + c.x + d - The cubic equation has 1, 2 or 3 real roots, and this function will return the number of real roots. + The cubic equation has 1, 2 or 3 real roots, and this function returns either 1 or 3, but in a special case, + 2 of the 3 roots found by this function will be equal to each other up to machine epsilon. + + The values of the roots, are returned by setting the values of the memory locations pointed to by t0, t1, and t2. In the case of three real roots, the roots themselves back in t0, t1 and t2. In the case of two real roots, a pair in t0, t1, and t2 will have the same value, and the other is a different one. - In the case of one real root, t0 will be the real root, and t1 + i * t2 will a pair of coplex-conjugated roots. + In the case of one real root, t0 will be the real root, and t1 +- i * t2 will a pair of complex-conjugated roots. The practical algorithm is followed by https://quarticequations.com - :param double a: Cubic constant. + :param double a: Cubic constant. :param double b: Cubic constant. :param double c: Cubic constant. :param double d: Cubic constant. @@ -513,7 +516,7 @@ cdef int solve_biquadratic(double a, double c, double e, double *t0, double *t1, the values of t2 and t3 will be undefined. If there is no real root, all values will be undefined. - :param double a: Biquadratic constant. + :param double a: Biquadratic constant. :param double c: Biquadratic constant. :param double e: Biquadratic constant. :param double t0: 1st root of the biquadratic. @@ -521,7 +524,7 @@ cdef int solve_biquadratic(double a, double c, double e, double *t0, double *t1, :param double t2: 3rd root of the biquadratic. :param double t3: 4th root of the biquadratic. :return: Number of real roots. - :rtype: int + :rtype: int """ cdef double s0, s1, sx0, sx1 @@ -542,7 +545,7 @@ cdef int solve_biquadratic(double a, double c, double e, double *t0, double *t1, t2[0] = sx0 t3[0] = sx1 return 4 - + # s0 < 0 <= s1, 2 real roots elif s1 >= 0: sx1 = sqrt(s1) @@ -562,7 +565,7 @@ cdef int _solve_depressed_quartic(double p, double q, double r, double *t0, doub cdef: int num double s0, sigma, A, B, sq_A, sq_B - + if q > 0: sigma = 1.0 else: @@ -690,7 +693,7 @@ cdef int solve_quartic(double a, double b, double c, double d, double e, The practical algorithm of Van der Waerden method is followed by https://quarticequations.com - :param double a: Qurtic constant. + :param double a: Qurtic constant. :param double b: Qurtic constant. :param double c: Qurtic constant. :param double d: Qurtic constant. diff --git a/raysect/primitive/torus.pyx b/raysect/primitive/torus.pyx index 21db4652..b284752b 100644 --- a/raysect/primitive/torus.pyx +++ b/raysect/primitive/torus.pyx @@ -50,14 +50,14 @@ cdef class Torus(Primitive): The torus is defined by major and minor radius. The major radius is the distance from the center of the tube to the center of the torus. The minor radius is the radius of the tube. - The center of the torus corresponds to the origin of the local co-ordinate system. + The center of the torus corresponds to the origin of the local coordinate system. The axis of revolution coincides with the z-axis, and The center of the torus tube lies on the x-y plane. :param float major_radius: Major radius of the torus in meters (default = 1.0). :param float minor_radius: Minor radius of the torus in meters (default = 0.5). :param Node parent: Scene-graph parent node or None (default = None). - :param AffineMatrix3D transform: An AffineMatrix3D defining the local co-ordinate system relative to the scene-graph parent (default = identity matrix). + :param AffineMatrix3D transform: An AffineMatrix3D defining the local coordinate system relative to the scene-graph parent (default = identity matrix). :param Material material: A Material object defining the torus's material (default = None). :param str name: A string specifying a user-friendly name for the torus (default = ""). @@ -197,14 +197,14 @@ cdef class Torus(Primitive): if num == 0: return None - + elif num == 1: # test the intersection points inside the ray search range [0, max_distance] if t[0] > ray.max_distance or t[0] < 0.0: return None else: t_closest = t[0] - + else: # sorting solutions in each number of them if num == 2: @@ -330,11 +330,10 @@ cdef class Torus(Primitive): # obtain local space vertices points = box.vertices() - # convert points to world space and build an enclosing world space bounding box - # a small degree of padding is added to avoid potential numerical accuracy issues + # convert points to world space box = BoundingBox3D() for point in points: - box.extend(point.transform(self.to_root()), BOX_PADDING) + box.extend(point.transform(self.to_root())) return box From 45f63d5191e4b32fd8ae5cb1d596c0c48da8573c Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Mon, 21 Jul 2025 13:57:14 -0400 Subject: [PATCH 14/19] =?UTF-8?q?=F0=9F=90=9B=20Fix=20intersection=20cachi?= =?UTF-8?q?ng=20and=20indexing=20in=20Torus=20class?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- raysect/primitive/torus.pxd | 15 +++++++++------ raysect/primitive/torus.pyx | 36 +++++++++++++++++++++++++++++++----- 2 files changed, 40 insertions(+), 11 deletions(-) diff --git a/raysect/primitive/torus.pxd b/raysect/primitive/torus.pxd index 5b2c7d48..9643552b 100644 --- a/raysect/primitive/torus.pxd +++ b/raysect/primitive/torus.pxd @@ -33,11 +33,14 @@ from raysect.core cimport Primitive, Point3D, Vector3D, Ray, Intersection cdef class Torus(Primitive): - cdef double _major_radius, _minor_radius - cdef bint _further_intersection - cdef double _next_t - cdef Point3D _cached_origin - cdef Vector3D _cached_direction - cdef Ray _cached_ray + cdef: + double _major_radius, _minor_radius + bint _further_intersection + int _next_t_index + int _num_t + double[4] _cached_t + Point3D _cached_origin + Vector3D _cached_direction + Ray _cached_ray cdef Intersection _generate_intersection(self, Ray ray, Point3D origin, Vector3D direction, double ray_distance) diff --git a/raysect/primitive/torus.pyx b/raysect/primitive/torus.pyx index b284752b..0b9818aa 100644 --- a/raysect/primitive/torus.pyx +++ b/raysect/primitive/torus.pyx @@ -91,7 +91,8 @@ cdef class Torus(Primitive): # initialise next intersection caching and control attributes self._further_intersection = False - self._next_t = 0.0 + self._next_t_index = 0 + self._num_t = 0 self._cached_origin = None self._cached_direction = None self._cached_ray = None @@ -233,15 +234,19 @@ cdef class Torus(Primitive): if t[0] > ray.max_distance or t[3] < 0.0: return None + # cache the all intersection points + self._num_t = num + self._cached_t = t + for i in range(num - 1): if t[i] >= 0.0: t_closest = t[i] if t[i + 1] <= ray.max_distance: self._further_intersection = True + self._next_t_index = i + 1 self._cached_ray = ray self._cached_origin = origin self._cached_direction = direction - self._next_t = t[i + 1] return self._generate_intersection(ray, origin, direction, t_closest) @@ -254,12 +259,33 @@ cdef class Torus(Primitive): cpdef Intersection next_intersection(self): + cdef: + double next_t + Intersection new_intersection + if not self._further_intersection: return None - # this is the 2nd intersection - self._further_intersection = False - return self._generate_intersection(self._cached_ray, self._cached_origin, self._cached_direction, self._next_t) + next_t = self._cached_t[self._next_t_index] + + # generate the next intersection. + new_intersection = self._generate_intersection( + self._cached_ray, + self._cached_origin, + self._cached_direction, + next_t, + ) + + # update the next intersection index + # if there are no more intersections, disable further intersection state + # and reset the next_t_index to 0 + if self._next_t_index < self._num_t - 1: + self._next_t_index += 1 + else: + self._further_intersection = False + self._next_t_index = 0 + + return new_intersection cdef Intersection _generate_intersection(self, Ray ray, Point3D origin, Vector3D direction, double ray_distance): From 052718ccc3dfdea03c7475800448a69018f76766 Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Mon, 21 Jul 2025 20:37:56 -0400 Subject: [PATCH 15/19] Update documentation to include Parabola and Torus in geometric primitives --- .../api_reference/primitives/geometric_primitives.rst | 4 ++++ docs/source/how_it_works.rst | 2 +- docs/source/primitives.rst | 11 ++++++++++- 3 files changed, 15 insertions(+), 2 deletions(-) diff --git a/docs/source/api_reference/primitives/geometric_primitives.rst b/docs/source/api_reference/primitives/geometric_primitives.rst index d0b833cb..a21d2b87 100644 --- a/docs/source/api_reference/primitives/geometric_primitives.rst +++ b/docs/source/api_reference/primitives/geometric_primitives.rst @@ -21,3 +21,7 @@ Geometric Primitives .. autoclass:: raysect.primitive.Parabola :members: radius, height :show-inheritance: + +.. autoclass:: raysect.primitive.Torus + :members: major_radius, minor_radius + :show-inheritance: diff --git a/docs/source/how_it_works.rst b/docs/source/how_it_works.rst index d64f5916..ef6994ff 100644 --- a/docs/source/how_it_works.rst +++ b/docs/source/how_it_works.rst @@ -58,7 +58,7 @@ Primitives Scenes in Raysect consist of primitives, which are the basic objects making up the scene. These are objects that rays can interact with, e.g light sources, lenses, mirrors, diffuse surfaces. Types of primitives: -* Mathematically defined surfaces and solids (i.e. sphere, box, cylinder, cone). +* Mathematically defined surfaces and solids (i.e. sphere, box, cylinder, cone, parabola, torus). * Constructive Solid Geometry Operators (union, intersect, subtract). * Tri-poly meshes optimised for millions of polygons, support instancing. Importers for STL and OBJ. diff --git a/docs/source/primitives.rst b/docs/source/primitives.rst index ac997661..1a94b7ae 100644 --- a/docs/source/primitives.rst +++ b/docs/source/primitives.rst @@ -3,7 +3,7 @@ Primitives ********** -The raysect primitives: sphere; box; cylinder; and cone. +The raysect primitives: sphere; box; cylinder; cone; parabola; and torus. .. image:: images/raysect_primitives.png :align: center @@ -30,6 +30,15 @@ Cone .. autoclass:: raysect.primitive.Cone +Parabola +~~~~~~~~ + +.. autoclass:: raysect.primitive.Parabola + +Torus +~~~~~ + +.. autoclass:: raysect.primitive.Torus ============== CSG Operations From 28e605da5702c5fc76d413e8fcb533cf4eb9a192 Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Tue, 22 Jul 2025 08:26:59 -0400 Subject: [PATCH 16/19] Add demo script for raysect geometric primitives. --- demos/raysect_primitives.py | 126 ++++++++++++++++++++++++++++++++++++ 1 file changed, 126 insertions(+) create mode 100644 demos/raysect_primitives.py diff --git a/demos/raysect_primitives.py b/demos/raysect_primitives.py new file mode 100644 index 00000000..9e6825fd --- /dev/null +++ b/demos/raysect_primitives.py @@ -0,0 +1,126 @@ +# External imports +from time import strftime + +from matplotlib import pyplot as plt + +# Raysect imports +from raysect.optical import Point3D, World, d65_white, rotate, translate +from raysect.optical.library import schott +from raysect.optical.material import Checkerboard, Lambert +from raysect.optical.observer import PinholeCamera, RGBAdaptiveSampler2D, RGBPipeline2D +from raysect.primitive import Box, Cone, Cylinder, Parabola, Sphere, Torus + +# 1. Create Primitives +# -------------------- + +# Box defining the ground plane +ground = Box( + lower=Point3D(-50, -0.01, -50), upper=Point3D(50, 0.0, 50), material=Lambert() +) + +# checker board wall that acts as emitter +emitter = Box( + lower=Point3D(-100, -100, 10), + upper=Point3D(100, 100, 10.1), + material=Checkerboard(4, d65_white, d65_white, 0.1, 2.0), +) + +# Primitive showcasing all geometric features +# Note that the primitives must be displaced slightly above the ground plane to prevent numerically issues that could +# cause a light leak at the intersection between the objects and the ground. +cylinder = Cylinder( + radius=1.5, + height=3.0, + transform=translate(1.5 * 3 + 1.0, 0.0001, 0) * rotate(0, 90, 0), + material=schott("N-BK7"), +) +cone = Cone( + radius=1.5, + height=3.0, + transform=translate(1.5 + 0.2, 0.0001, 0) * rotate(0, 90, 0), + material=schott("N-BK7"), +) +sphere = Sphere( + radius=1.5, + transform=translate(-1.5 - 0.2, 1.5 + 0.0001, 0), + material=schott("N-BK7"), +) +box = Box( + lower=Point3D(-1.5, 0.0, -1.5), + upper=Point3D(1.5, 3.0, 1.5), + transform=translate(-1.5 * 3 - 1.0, 0.0001, 0), + material=schott("N-BK7"), +) +parabola = Parabola( + radius=2.0, + height=1.0, + transform=translate(2.5, 1.0 + 0.0001, -5.0) * rotate(0, -90, 0), + material=schott("N-BK7"), +) +torus = Torus( + major_radius=1.0, + minor_radius=0.5, + transform=translate(-2.5, 0.5 + 0.0001, -5.0) * rotate(0, 90, 0), + material=schott("N-BK7"), +) + + +# 2. Add Observer +# --------------- + +# Process the ray-traced spectra with the RGB pipeline. +rgb = RGBPipeline2D(display_unsaturated_fraction=0.96) +sampler = RGBAdaptiveSampler2D( + rgb, ratio=10, fraction=0.2, min_samples=2000, cutoff=0.01 +) + +# camera +camera = PinholeCamera( + (512, 512), pipelines=[rgb], transform=translate(-7, 12, -15) * rotate(-25, -40, 0) +) + +# camera - pixel sampling settings +camera.fov = 45 +camera.pixel_samples = 250 + +# camera - ray sampling settings +camera.spectral_rays = 15 +camera.spectral_bins = 15 +camera.ray_max_depth = 100 +camera.ray_extinction_prob = 0.1 +camera.min_wavelength = 375.0 +camera.max_wavelength = 740.0 + + +# 3. Build Scenegraph +# ------------------- + +world = World() + +ground.parent = world +emitter.parent = world +camera.parent = world +cylinder.parent = world +cone.parent = world +sphere.parent = world +box.parent = world +parabola.parent = world +torus.parent = world + +# 4. Observe() +# ------------ +name = "raysect_primitives" +timestamp = strftime("%Y-%m-%d_%H-%M-%S") +render_pass = 1 +plt.ion() +while not camera.render_complete: + print(f"Rendering pass {render_pass}...") + camera.observe() + rgb.save(f"{name}_{timestamp}_pass_{render_pass}.png") + render_pass += 1 + print() + +# display final result +plt.ioff() +rgb.display() +plt.show() From 4c5c4810e3759be1f64de18445bc2caca384c8da Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Tue, 22 Jul 2025 08:30:06 -0400 Subject: [PATCH 17/19] Update raysect_primitives.png image for including all geometric primitives --- docs/source/images/raysect_primitives.png | Bin 290618 -> 214353 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/docs/source/images/raysect_primitives.png b/docs/source/images/raysect_primitives.png index 0439ab9320057d44eaa53432c78721e92f100ddd..cd2301f3ef492e9c132fe14b9154da0923edb0be 100644 GIT binary patch literal 214353 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zscsmLbDAd|NCQtklr+6=MuHhWFIe%#&`JMLsU0XC)IQQ=R=JZ5iRK2yO*RbT-z;a${k!iilD(9fU jQFRFBsb}gVC!+r!UfQG!-;)wP00000NkvXXu0mjf6nQDF From b46559a09a5aba215f1bec99cf723d9753fdef20 Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Tue, 22 Jul 2025 08:49:43 -0400 Subject: [PATCH 18/19] move raysect_primitives.py to demos/primitives --- demos/{ => primitives}/raysect_primitives.py | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename demos/{ => primitives}/raysect_primitives.py (100%) diff --git a/demos/raysect_primitives.py b/demos/primitives/raysect_primitives.py similarity index 100% rename from demos/raysect_primitives.py rename to demos/primitives/raysect_primitives.py From 22aa40c83e13e694ec0e62ff43068521229c23e4 Mon Sep 17 00:00:00 2001 From: munechika-koyo Date: Tue, 22 Jul 2025 14:25:18 -0400 Subject: [PATCH 19/19] Add torus.pyx and torus.pxd to source files in meson.build --- raysect/primitive/meson.build | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/raysect/primitive/meson.build b/raysect/primitive/meson.build index 6dab2462..1f14a347 100644 --- a/raysect/primitive/meson.build +++ b/raysect/primitive/meson.build @@ -5,8 +5,8 @@ target_path = 'raysect/primitive' # source files py_files = ['__init__.py'] -pyx_files = ['box.pyx', 'cone.pyx', 'csg.pyx', 'cylinder.pyx', 'parabola.pyx', 'sphere.pyx', 'utility.pyx'] -pxd_files = ['__init__.pxd', 'box.pxd', 'cone.pxd', 'csg.pxd', 'cylinder.pxd', 'parabola.pxd', 'sphere.pxd', 'utility.pxd'] +pyx_files = ['box.pyx', 'cone.pyx', 'csg.pyx', 'cylinder.pyx', 'parabola.pyx', 'sphere.pyx', 'torus.pyx', 'utility.pyx'] +pxd_files = ['__init__.pxd', 'box.pxd', 'cone.pxd', 'csg.pxd', 'cylinder.pxd', 'parabola.pxd', 'sphere.pxd', 'torus.pxd', 'utility.pxd'] data_files = [] # compile cython