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shapes.cpp
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//
// Created by Bradley Austin Davis on 2016/05/26
// Copyright 2013-2016 High Fidelity, Inc.
//
// Distributed under the Apache License, Version 2.0.
// See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html
//
#include "shapes.h"
namespace geometry {
using glm::vec3;
// The golden ratio
static const float PHI = 1.61803398874f;
Solid<3> tesselate(const Solid<3>& solid_, int count) {
Solid<3> solid = solid_;
float length = glm::length(solid.vertices[0]);
for (int i = 0; i < count; ++i) {
Solid<3> result{ solid.vertices, {} };
result.vertices.reserve(solid.vertices.size() + solid.faces.size() * 3);
for (size_t f = 0; f < solid.faces.size(); ++f) {
Index baseVertex = (Index)result.vertices.size();
const Face<3>& oldFace = solid.faces[f];
const vec3& a = solid.vertices[oldFace[0]];
const vec3& b = solid.vertices[oldFace[1]];
const vec3& c = solid.vertices[oldFace[2]];
vec3 ab = glm::normalize(a + b) * length;
vec3 bc = glm::normalize(b + c) * length;
vec3 ca = glm::normalize(c + a) * length;
result.vertices.push_back(ab);
result.vertices.push_back(bc);
result.vertices.push_back(ca);
result.faces.push_back(Face<3>{ { oldFace[0], baseVertex, baseVertex + 2 } });
result.faces.push_back(Face<3>{ { baseVertex, oldFace[1], baseVertex + 1 } });
result.faces.push_back(Face<3>{ { baseVertex + 1, oldFace[2], baseVertex + 2 } });
result.faces.push_back(Face<3>{ { baseVertex, baseVertex + 1, baseVertex + 2 } });
}
solid = result;
}
return solid;
}
const Solid<3>& tetrahedron() {
static const auto A = vec3(1, 1, 1);
static const auto B = vec3(1, -1, -1);
static const auto C = vec3(-1, 1, -1);
static const auto D = vec3(-1, -1, 1);
static const Solid<3> TETRAHEDRON = Solid<3>{ { A, B, C, D },
FaceVector<3>{
Face<3>{ { 0, 1, 2 } },
Face<3>{ { 3, 1, 0 } },
Face<3>{ { 2, 3, 0 } },
Face<3>{ { 2, 1, 3 } },
} }
.fitDimension(0.5f);
return TETRAHEDRON;
}
const Solid<4>& cube() {
static const auto A = vec3(1, 1, 1);
static const auto B = vec3(-1, 1, 1);
static const auto C = vec3(-1, 1, -1);
static const auto D = vec3(1, 1, -1);
static const Solid<4> CUBE = Solid<4>{ { A, B, C, D, -A, -B, -C, -D },
FaceVector<4>{
Face<4>{ { 3, 2, 1, 0 } },
Face<4>{ { 0, 1, 7, 6 } },
Face<4>{ { 1, 2, 4, 7 } },
Face<4>{ { 2, 3, 5, 4 } },
Face<4>{ { 3, 0, 6, 5 } },
Face<4>{ { 4, 5, 6, 7 } },
} }
.fitDimension(0.5f);
return CUBE;
}
const Solid<3>& octahedron() {
static const auto A = vec3(0, 1, 0);
static const auto B = vec3(0, -1, 0);
static const auto C = vec3(0, 0, 1);
static const auto D = vec3(0, 0, -1);
static const auto E = vec3(1, 0, 0);
static const auto F = vec3(-1, 0, 0);
static const Solid<3> OCTAHEDRON = Solid<3>{ { A, B, C, D, E, F },
FaceVector<3>{
Face<3>{ {
0,
2,
4,
} },
Face<3>{ {
0,
4,
3,
} },
Face<3>{ {
0,
3,
5,
} },
Face<3>{ {
0,
5,
2,
} },
Face<3>{ {
1,
4,
2,
} },
Face<3>{ {
1,
3,
4,
} },
Face<3>{ {
1,
5,
3,
} },
Face<3>{ {
1,
2,
5,
} },
} }
.fitDimension(0.5f);
return OCTAHEDRON;
}
const Solid<5>& dodecahedron() {
static const float P = PHI;
static const float IP = 1.0f / PHI;
static const vec3 A = vec3(IP, P, 0);
static const vec3 B = vec3(-IP, P, 0);
static const vec3 C = vec3(-1, 1, 1);
static const vec3 D = vec3(0, IP, P);
static const vec3 E = vec3(1, 1, 1);
static const vec3 F = vec3(1, 1, -1);
static const vec3 G = vec3(-1, 1, -1);
static const vec3 H = vec3(-P, 0, IP);
static const vec3 I = vec3(0, -IP, P);
static const vec3 J = vec3(P, 0, IP);
static const Solid<5> DODECAHEDRON = Solid<5>{ {
A, B, C, D, E, F, G, H, I, J, -A, -B, -C, -D, -E, -F, -G, -H, -I, -J,
},
FaceVector<5>{
Face<5>{ { 0, 1, 2, 3, 4 } },
Face<5>{ { 0, 5, 18, 6, 1 } },
Face<5>{ { 1, 6, 19, 7, 2 } },
Face<5>{ { 2, 7, 15, 8, 3 } },
Face<5>{ { 3, 8, 16, 9, 4 } },
Face<5>{ { 4, 9, 17, 5, 0 } },
Face<5>{ { 14, 13, 12, 11, 10 } },
Face<5>{ { 11, 16, 8, 15, 10 } },
Face<5>{ { 12, 17, 9, 16, 11 } },
Face<5>{ { 13, 18, 5, 17, 12 } },
Face<5>{ { 14, 19, 6, 18, 13 } },
Face<5>{ { 10, 15, 7, 19, 14 } },
} }
.fitDimension(0.5f);
return DODECAHEDRON;
}
const Solid<3>& icosahedron() {
static const float N = 1.0f / PHI;
static const float P = 1.0f;
static const auto A = vec3(N, P, 0);
static const auto B = vec3(-N, P, 0);
static const auto C = vec3(0, N, P);
static const auto D = vec3(P, 0, N);
static const auto E = vec3(P, 0, -N);
static const auto F = vec3(0, N, -P);
static const Solid<3> ICOSAHEDRON =
Solid<3>{ {
A,
B,
C,
D,
E,
F,
-A,
-B,
-C,
-D,
-E,
-F,
},
FaceVector<3>{
Face<3>{ { 1, 2, 0 } }, Face<3>{ { 2, 3, 0 } }, Face<3>{ { 3, 4, 0 } }, Face<3>{ { 4, 5, 0 } }, Face<3>{ { 5, 1, 0 } },
Face<3>{ { 1, 10, 2 } }, Face<3>{ { 11, 2, 10 } }, Face<3>{ { 2, 11, 3 } }, Face<3>{ { 7, 3, 11 } }, Face<3>{ { 3, 7, 4 } },
Face<3>{ { 8, 4, 7 } }, Face<3>{ { 4, 8, 5 } }, Face<3>{ { 9, 5, 8 } }, Face<3>{ { 5, 9, 1 } }, Face<3>{ { 10, 1, 9 } },
Face<3>{ { 8, 7, 6 } }, Face<3>{ { 9, 8, 6 } }, Face<3>{ { 10, 9, 6 } }, Face<3>{ { 11, 10, 6 } }, Face<3>{ { 7, 11, 6 } },
} }
.fitDimension(0.5f);
return ICOSAHEDRON;
}
} // namespace geometry