math_common.cpp

#include "math_common.h"

glm::vec3 FrustumUtils::ndc_to_world(glm::vec3 ndc, glm::mat4 proj_inv, glm::mat4 view_inv) {
	glm::vec4 view_space_coord = proj_inv * glm::vec4(ndc, 1.0f);
	view_space_coord = view_space_coord / view_space_coord.w;
	glm::vec4 world_space_coord = view_inv * view_space_coord;
	return world_space_coord;
}

// in world space
FrustumUtils::Frustum FrustumUtils::view_frustum_vertices(glm::mat4 proj_inv, glm::mat4 view_inv) {
	Frustum f;
	/*near top left*/		f[0] = ndc_to_world(glm::vec3(-1.0f, -1.0f, 0.0f), proj_inv, view_inv);
	/*near bottom left*/	f[1] = ndc_to_world(glm::vec3(-1.0f, 1.0f, 0.0f), proj_inv, view_inv);
	/*near bottom right*/	f[2] = ndc_to_world(glm::vec3(1.0f, 1.0f, 0.0f), proj_inv, view_inv);
	/*near top right*/		f[3] = ndc_to_world(glm::vec3(1.0f, -1.0f, 0.0f), proj_inv, view_inv);
	/*far top left*/		f[4] = ndc_to_world(glm::vec3(-1.0f, -1.0f, 1.0f), proj_inv, view_inv);
	/*far bottom left*/		f[5] = ndc_to_world(glm::vec3(-1.0f, 1.0f, 1.0f), proj_inv, view_inv);
	/*far bottom right*/	f[6] = ndc_to_world(glm::vec3(1.0f, 1.0f, 1.0f), proj_inv, view_inv);
	/*far top right*/		f[7] = ndc_to_world(glm::vec3(1.0f, -1.0f, 1.0f), proj_inv, view_inv);

	return f;
}


void FrustumUtils::bounding_sphere(const Frustum& f, glm::vec3& center, float& radius) {
	auto length2 = [](glm::vec3 v) -> float {
		return glm::dot(v, v);
	};
	glm::vec3 center_far = (f[6] + f[4]) * 0.5f;
	float b2 = length2(center_far - f[4]);
	float r2 = length2(center_far - f[0]);
	if (r2 > b2) {
		// can't envelop near-plane vertices
		glm::vec3 center_near = (f[2] + f[0]) * 0.5f;
		float a2 = length2(center_near - f[0]);
		float H = glm::length(center_near - center_far);
		float c = (b2 - a2 - H*H) / (2.0f * H);
		center = glm::mix(center_near, center_far, (H + c) / H);
		radius = glm::sqrt(b2 + c * c);
	}
	else {
		center = center_far;
		radius = glm::sqrt(b2);
	}
}

glm::vec4 FrustumUtils::plane(glm::vec3 a, glm::vec3 b, glm::vec3 c) {
	glm::vec3 cross = glm::cross(b - a, c - a);
	float len = glm::length(cross);
	if (len < 10E-5) {
		return glm::vec4(0.0f, 0.0f, 0.0f, 0.0f);
	}
	glm::vec3 n = cross / len;
	float d = -glm::dot(n, a);
	return glm::vec4(n, d);
}