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#include "raytracer/raytracer.h"
// vector operations on 4d vectors,
// reference: https://hollasch.github.io/ray4/Four-Space_Visualization_of_4D_Objects.html#chapter5
glm::vec4 cross4(
glm::vec4 u,
glm::vec4 v,
glm::vec4 w) {
float a = (v[0] * w[1]) - (v[1] * w[0]);
float b = (v[0] * w[2]) - (v[2] * w[0]);
float c = (v[0] * w[3]) - (v[3] * w[0]);
float d = (v[1] * w[2]) - (v[2] * w[1]);
float e = (v[1] * w[3]) - (v[3] * w[1]);
float f = (v[2] * w[3]) - (v[3] * w[2]);
glm::vec4 result;
result[0] = (u[1] * f) - (u[2] * e) + (u[3] * d);
result[1] = -(u[0] * f) + (u[2] * c) - (u[3] * b);
result[2] = (u[0] * e) - (u[1] * c) + (u[3] * a);
result[3] = -(u[0] * d) + (u[1] * b) - (u[2] * a);
return result;
}
glm::vec4 dot4(
glm::vec4 u,
glm::vec4 v) {
return {u[0] * v[0], u[1] * v[1], u[2] * v[2], u[3] * v[3]};
}
glm::mat4 getViewMatrix4(
glm::vec4 fromPoint,
glm::vec4 toPoint,
glm::vec4 upVector,
glm::vec4 lookVector) {
// calculate e3 basis vector, the transformation col of view matrix
if (glm::distance(fromPoint, toPoint) < 0.0001f) {
throw std::runtime_error("fromPoint and toPoint are the same");
}
glm::vec4 e3 = glm::normalize(fromPoint - toPoint);
// calculate e2 basis vector, from the combinatory cross of up and over with e3
glm::vec4 e2 = cross4(upVector, lookVector, e3);
e2 = glm::normalize(e2);
if (glm::distance(e2, glm::vec4{0, 0, 0, 0}) < 0.0001f) {
throw std::runtime_error("invalid up vector");
}
// calculate e1 basis vector, from the cross of only the over vector
glm::vec4 e1 = cross4(lookVector, e3, e2);
e1 = glm::normalize(e1);
if (glm::distance(e1, glm::vec4{0, 0, 0, 0}) < 0.0001f) {
throw std::runtime_error("invalid over vector");
}
// calculate e0 basis vector, the 4d orthogonal vector to the other 3 bases
glm::vec4 e0 = cross4(e3, e2, e1);
e0 = glm::normalize(e0);
return {e2, e1, e0, e3};
}
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