Python - Triangles - Intersecting a Ray with a Triangle - ray strikes

The Ray Tracer Challenge:
A Test-Driven Guide to Your First 3D Renderer
楽天 紀伊国屋書店

開発環境

• macOS Mojave - Apple (OS)
• Emacs (Text Editor)
• Windows 10 Pro (OS)
• Visual Studio Code (Text Editor)
• Python 3.7 (プログラミング言語)
• GIMP (ビットマップ画像編集・加工ソフトウェア、PPM形式(portable pixmap)の画像用)

The Ray Tracer Challenge: A Test-Driven Guide to Your First 3D Renderer (Jamis Buck(著)、Pragmatic Bookshelf)、Chapter 15(Triangles)のTriangles、Test #3 to 7(Intersecting a Ray with a Triangle)、ray strikesを取り組んでみる。

コード

triangles_test.py

#!/usr/bin/env python3
from unittest import TestCase, main
from tuples import Point, Vector
from triangles import Triangle
from rays import Ray


class TriangleTest(TestCase):
    def setUp(self):
        pass

    def tearDown(self):
        pass

    def test_init(self):
        point1 = Point(0, 1, 0)
        point2 = Point(-1, 0, 0)
        point3 = Point(1, 0, 0)
        triangle = Triangle(point1, point2, point3)
        self.assertEqual(triangle.point1, point1)
        self.assertEqual(triangle.point2, point2)
        self.assertEqual(triangle.point3, point3)
        self.assertEqual(triangle.edge1, Vector(-1, -1, 0))
        self.assertEqual(triangle.edge2, Vector(1, -1, 0))
        self.assertEqual(triangle.normal, Vector(0, 0, -1))

    def test_finding_normal_vector(self):
        triangle = Triangle(Point(0, 1, 0), Point(-1, 0, 0), Point(1, 0, 0))
        normal_vector1 = triangle.local_normal_at(Point(0, 0.5, 0))
        normal_vector2 = triangle.local_normal_at(Point(-0.5, 0.75, 0))
        normal_vector3 = triangle.local_normal_at(Point(0.5, 0.25, 0))
        self.assertEqual(normal_vector1, triangle.normal)
        self.assertEqual(normal_vector2, triangle.normal)
        self.assertEqual(normal_vector3, triangle.normal)

    def test_intersecting_ray_parallel(self):
        triangle = Triangle(Point(0, 1, 0), Point(-1, 0, 0), Point(1, 0, 0))
        ray = Ray(Point(0, -1, -2), Vector(0, 1, 0))
        intersections = triangle.intersect(ray)
        self.assertEqual(len(intersections), 0)

    def test_ray_misses_p1_p3_edge(self):
        triangle = Triangle(Point(0, 1, 0), Point(-1, 0, 0), Point(1, 0, 0))
        ray = Ray(Point(1, 1, -2), Vector(0, 0, 1))
        intersections = triangle.intersect(ray)
        self.assertEqual(len(intersections), 0)

    def test_ray_misses_p1_p2_edge(self):
        triangle = Triangle(Point(0, 1, 0), Point(-1, 0, 0), Point(1, 0, 0))
        ray = Ray(Point(-1, 1, -2), Vector(0, 0, 1))
        intersections = triangle.intersect(ray)
        self.assertEqual(len(intersections), 0)

    def test_ray_misses_p2_p3_edge(self):
        triangle = Triangle(Point(0, 1, 0), Point(-1, 0, 0), Point(1, 0, 0))
        ray = Ray(Point(0, -1, -2), Vector(0, 0, 1))
        intersections = triangle.intersect(ray)
        self.assertEqual(len(intersections), 0)

    def test_ray_strikes(self):
        triangle = Triangle(Point(0, 1, 0), Point(-1, 0, 0), Point(1, 0, 0))
        ray = Ray(Point(0, 0.5, -2), Vector(0, 0, 1))
        intersections = triangle.intersect(ray)
        self.assertEqual(len(intersections), 1)
        self.assertEqual(intersections[0].t, 2)


if __name__ == '__main__':
    main()

triangles.py

from tuples import EPSILON
from intersections import Intersections, Intersection


class Triangle:
    def __init__(self, point1, point2, point3):
        self.point1 = point1
        self.point2 = point2
        self.point3 = point3
        self.edge1 = point2 - point1
        self.edge2 = point3 - point1
        self.normal = self.edge2.cross(self.edge1).normalize()

    def local_normal_at(self, point):
        return self.normal

    def intersect(self, ray):
        dir_cross_edge2 = ray.direction.cross(self.edge2)
        det = self.edge1.dot(dir_cross_edge2)
        if abs(det) < EPSILON:
            return Intersections()
        f = 1.0 / det
        point1_to_origin = ray.origin - self.point1
        u = f * point1_to_origin.dot(dir_cross_edge2)
        if u < 0 or u > 1:
            return Intersections()
        origin_cross_edge1 = point1_to_origin.cross(self.edge1)
        v = f * ray.direction.dot(origin_cross_edge1)
        if v < 0 or (u + v) > 1:
            return Intersections()
        t = f * self.edge2.dot(origin_cross_edge1)
        return Intersections(Intersection(t, self))

入出力結果(Bash、cmd.exe(コマンドプロンプト)、Terminal、Jupyter(IPython))

C:\Users\...>py triangles_test.py
.......
----------------------------------------------------------------------
Ran 7 tests in 0.001s

OK

C:\Users\...>