objlib.py

#
# Objects Library
# All the objects and their interset methods will be defined here.
#

import numpy as np

def add_cone():
    # Define cone here.
    # Method is unfinished
    return None

def intersect_cone():
    # Define cone here.
    # Method is unfinished
    return None

def add_cylinder():
    # Define cone here.
    # Method is unfinished
    return None

def intersect_cylinder():
    # Define cone here.
    # Method is unfinished
    return None

def add_cube():
    # Define cone here.
    # Method is unfinished
    return None

def intersect_cube():
    # Define cone here.
    # Method is unfinished
    return None

def add_pyramid():
    # Define cone here.
    # Method is unfinished
    return None

def intersect_pyramid():
    # Define cone here.
    # Method is unfinished
    return None

def add_sphere(position, radius, color):
    return dict(type='sphere', position=np.array(position), 
        radius=np.array(radius), color=np.array(color), reflection=.5)


def intersect_sphere(O, D, S, R):
    # Return the distance from O to the intersection of the ray (O, D) with the 
    # sphere (S, R), or +inf if there is no intersection.
    # O and S are 3D points, D (direction) is a normalized vector, R is a scalar.
    a = np.dot(D, D)
    OS = O - S
    b = 2 * np.dot(D, OS)
    c = np.dot(OS, OS) - R * R
    disc = b * b - 4 * a * c
    if disc > 0:
        distSqrt = np.sqrt(disc)
        q = (-b - distSqrt) / 2.0 if b < 0 else (-b + distSqrt) / 2.0
        t0 = q / a
        t1 = c / q
        t0, t1 = min(t0, t1), max(t0, t1)
        if t1 >= 0:
            return t1 if t0 < 0 else t0
    return np.inf

    
def add_plane(position, normal, color_plane0, color_plane1):
    return dict(type='plane', position=np.array(position), 
        normal=np.array(normal),
        color=lambda M: (color_plane0 
            if (int(M[0] * 2) % 2) == (int(M[2] * 2) % 2) else color_plane1),
        diffuse_c=.75, specular_c=.5, reflection=.25)


def intersect_plane(O, D, P, N):
    # Return the distance from O to the intersection of the ray (O, D) with the 
    # plane (P, N), or +inf if there is no intersection.
    # O and P are 3D points, D and N (normal) are normalized vectors.
    denom = np.dot(D, N)
    if np.abs(denom) < 1e-6:
        return np.inf
    d = np.dot(P - O, N) / denom
    if d < 0:
        return np.inf
    return d