[Math/MathUtils] Added a Fibonacci sphere points computation

- This allows computing evenly distributed points around a unit sphere, and will be useful for some algorithms
Razakhel · Feb 2, 2024 · e96b218 · e96b218
1 parent 7b999ca
commit e96b218
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diff --git a/include/RaZ/Math/MathUtils.hpp b/include/RaZ/Math/MathUtils.hpp
@@ -3,11 +3,13 @@
 #ifndef RAZ_MATHUTILS_HPP
 #define RAZ_MATHUTILS_HPP
 
+#include "RaZ/Math/Constants.hpp"
 #include "RaZ/Math/Vector.hpp"
 
 #include <algorithm>
 #include <cassert>
 #include <type_traits>
+#include <vector>
 
 namespace Raz::MathUtils {
 
@@ -162,6 +164,23 @@ void computeOrthonormalBasis(const Vec3<T>& input, Vec3<T>& axis2, Vec3<T>& axis
   axis3 = Vec3<T>(b, sign + input.y() * input.y() * a, -input.y());
 }
 
+/// Computes points on the Fibonacci sphere, giving evenly distributed points around a unit sphere.
+/// \param pointCount Number of points to compute.
+/// \return Points on the Fibonacci sphere. All vectors are of length 1.
+inline std::vector<Vec3f> computeFibonacciSpherePoints(std::size_t pointCount) {
+  std::vector<Vec3f> fiboPoints(pointCount);
+
+  for (std::size_t i = 0; i < pointCount; ++i) {
+    const float theta  = 2.f * Pi<float> * static_cast<float>(i) / GoldenRatio<float>;
+    const float cosPhi = 1.f - 2.f * (static_cast<float>(i) + 0.5f) / static_cast<float>(pointCount);
+    const float sinPhi = std::sqrt(1.f - cosPhi * cosPhi);
+
+    fiboPoints[i] = Vec3f(std::cos(theta) * sinPhi, cosPhi, std::sin(theta) * sinPhi);
+  }
+
+  return fiboPoints;
+}
+
 } // namespace Raz::MathUtils
 
 #endif // RAZ_MATHUTILS_HPP
diff --git a/tests/src/RaZ/Math/MathUtils.cpp b/tests/src/RaZ/Math/MathUtils.cpp
@@ -145,3 +145,38 @@ TEST_CASE("MathUtils orthonormal basis") {
   CHECK(axis3 == Raz::Vec3f(0.211324856f, -0.788675f, 0.577350259f));
   CHECK(axis2.dot(axis3) == 0.f);
 }
+
+TEST_CASE("MathUtils Fibonacci sphere") {
+  std::vector<Raz::Vec3f> fiboPoints = Raz::MathUtils::computeFibonacciSpherePoints(0);
+  CHECK(fiboPoints.empty());
+
+  fiboPoints = Raz::MathUtils::computeFibonacciSpherePoints(1);
+  REQUIRE(fiboPoints.size() == 1);
+  CHECK_THAT(fiboPoints[0], IsNearlyEqualToVector(Raz::Vec3f(1.f, 0.f, 0.f)));
+
+  fiboPoints = Raz::MathUtils::computeFibonacciSpherePoints(2);
+  REQUIRE(fiboPoints.size() == 2);
+  CHECK_THAT(fiboPoints[0], IsNearlyEqualToVector(Raz::Vec3f(0.8660253f, 0.5f, 0.f)));
+  CHECK_THAT(fiboPoints[1], IsNearlyEqualToVector(Raz::Vec3f(-0.6385802f, -0.5, -0.5849917f)));
+
+  fiboPoints = Raz::MathUtils::computeFibonacciSpherePoints(3);
+  REQUIRE(fiboPoints.size() == 3);
+  CHECK_THAT(fiboPoints[0], IsNearlyEqualToVector(Raz::Vec3f(0.745356f, 0.6666666f, 0.f)));
+  CHECK_THAT(fiboPoints[1], IsNearlyEqualToVector(Raz::Vec3f(-0.7373688f, 0.f, -0.6754903f)));
+  CHECK_THAT(fiboPoints[2], IsNearlyEqualToVector(Raz::Vec3f(0.0651632f, -0.6666666f, 0.742502f)));
+
+  fiboPoints = Raz::MathUtils::computeFibonacciSpherePoints(4);
+  REQUIRE(fiboPoints.size() == 4);
+  CHECK_THAT(fiboPoints[0], IsNearlyEqualToVector(Raz::Vec3f(0.6614378f, 0.75f, 0.f)));
+  CHECK_THAT(fiboPoints[1], IsNearlyEqualToVector(Raz::Vec3f(-0.7139543f, 0.25f, -0.6540406f)));
+  CHECK_THAT(fiboPoints[2], IsNearlyEqualToVector(Raz::Vec3f(0.0846495f, -0.25f, 0.9645385f)));
+  CHECK_THAT(fiboPoints[3], IsNearlyEqualToVector(Raz::Vec3f(0.4024442f, -0.75f, -0.5249176f)));
+
+  fiboPoints = Raz::MathUtils::computeFibonacciSpherePoints(5);
+  REQUIRE(fiboPoints.size() == 5);
+  CHECK_THAT(fiboPoints[0], IsNearlyEqualToVector(Raz::Vec3f(0.6f, 0.8f, 0.f)));
+  CHECK_THAT(fiboPoints[1], IsNearlyEqualToVector(Raz::Vec3f(-0.6758097f, 0.3999999f, -0.619097f)));
+  CHECK_THAT(fiboPoints[2], IsNearlyEqualToVector(Raz::Vec3f(0.0874256f, 0.f, 0.996171f)));
+  CHECK_THAT(fiboPoints[3], IsNearlyEqualToVector(Raz::Vec3f(0.5576431f, -0.3999999f, -0.7273473f)));
+  CHECK_THAT(fiboPoints[4], IsNearlyEqualToVector(Raz::Vec3f(-0.5908281f, -0.7999999f, 0.104509f)));
+}