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#include "raytracer/raytracer.h"
/**
* @brief This source file handles intersection calculations to be used by the ray tracer.
* The implementation for findIntersection in the RayTracer namespace is at the end of the file.
*/
// TODO: implement mesh
glm::vec4 intersectCircle(
glm::vec4 p,
glm::vec4 d,
const RenderShapeData& shape)
{
// implicit: x^2 + y^2 + z^2 - r^2 = 0, all directions
float radius = 0.5f;
float a = d.x*d.x + d.y*d.y + d.z*d.z;
float b = 2.f * (p.x*d.x + p.y*d.y + p.z*d.z);
float c = p.x*p.x + p.y*p.y + p.z*p.z - radius*radius;
float discriminant = b*b - 4*a*c;
if (discriminant < 0) // no solution
{
return glm::vec4(0.f);
}
float t1 = (-b - std::sqrt(discriminant)) / (2.f*a);
float t2 = (-b + std::sqrt(discriminant)) / (2.f*a);
if (t1 <= 0 && t2 <= 0) // both behind camera
{
return glm::vec4(0.f);
} else if (t1 <= 0) // t2 in front of camera
{
return p + t2*d;
} else if (t2 <= 0) // t1 in front of camera
{
return p + t1*d;
} else {
float t = std::min(t1, t2);
return p + t*d; // want best intersection point
}
}
glm::vec4 intersectCone(
glm::vec4 p,
glm::vec4 d,
const RenderShapeData& shape)
{
float t = FINF;
// implicit: x^2 + y^2 - z^2 = 0, conic top
float radius = 0.5f;
float a = d.x*d.x + d.z*d.z - .25f*(d.y*d.y);
float b = 2.f*(p.x*d.x + p.z*d.z) - .5f*(p.y*d.y) + .25f*d.y;
float c = p.x*p.x + p.z*p.z - .25f*(p.y*p.y) + .25f*p.y - 1/16.f;
float discriminant = b*b - 4*a*c;
if (discriminant >= 0)
{
float t1 = (-b - std::sqrt(discriminant)) / (2.f*a);
float t2 = (-b + std::sqrt(discriminant)) / (2.f*a);
auto p1Top = p + t1 * d;
if (
t1 > 0 &&
p1Top.y >= -.5f && p1Top.y <= .5f)
{
t = std::min(t1, t);
}
auto p2Top = p + t2 * d;
if (
t2 > 0 &&
p2Top.y >= -.5f && p2Top.y <= .5f)
{
t = std::min(t2, t);
}
}
// implicit p_y + t*d_y = -.5f, top base
float tBase = (- .5f - p.y) / d.y;
auto pBase = p + tBase * d;
if (
tBase > 0 &&
pBase.x*pBase.x + pBase.z*pBase.z <= radius*radius
)
{
t = std::min(t, tBase);
}
return t == FINF ? glm::vec4(0.f) : p + t*d;
}
glm::vec4 intersectCylinder(
glm::vec4 p,
glm::vec4 d,
const RenderShapeData& shape)
{
float t = FINF;
// implicit: x^2 + z^2 = 0, y between -.5, 5 rectuangular side
float radius = 0.5f;
float a = d.x*d.x + d.z*d.z;
float b = 2.f * (p.x*d.x + p.z*d.z);
float c = p.x*p.x + p.z*p.z - radius*radius;
float discriminant = b*b - 4*a*c;
if (discriminant >= 0)
{
float t1 = (-b - std::sqrt(discriminant)) / (2.f*a);
float t2 = (-b + std::sqrt(discriminant)) / (2.f*a);
auto p1Top = p + t1 * d;
if (
t1 > 0 &&
p1Top.y >= -.5f && p1Top.y <= .5f)
{
t = std::min(t1, t);
}
auto p2Top = p + t2 * d;
if (
t2 > 0 &&
p2Top.y >= -.5f && p2Top.y <= .5f)
{
t = std::min(t2, t);
}
}
// implicit p_y + t*d_y = -.5f, top base
float tTop = (.5f - p.y) / d.y;
auto pTop = p + tTop * d;
if (
tTop > 0 &&
pTop.x*pTop.x + pTop.z*pTop.z <= radius*radius
)
{
t = std::min(t, tTop);
}
// implicit p_y + t*d_y = -.5f, top base
float tBase = (- .5f - p.y) / d.y;
auto pBase = p + tBase * d;
if (
tBase > 0 &&
pBase.x*pBase.x + pBase.z*pBase.z <= radius*radius
)
{
t = std::min(t, tBase);
}
return t == FINF ? glm::vec4(0.f) : p + t*d;
}
glm::vec4 intersectCube (
glm::vec4 p,
glm::vec4 d,
const RenderShapeData& shape)
{
// float t = FINF;
float apothem = .5f;
// start with x-dir
float tmin = (-apothem - p.x) / d.x;
float tmax = (apothem - p.x) / d.x;
// see if it hits top or bottom
if (tmin > tmax)
{
std::swap(tmin, tmax);
}
// y-dir
float tymin = (-apothem - p.y) / d.y;
float tymax = (apothem - p.y) / d.y;
if (tymin > tymax)
{
std::swap(tymin, tymax);
}
if ((tmin > tymax) || (tymin > tmax))
{ // no hit
return glm::vec4(0.f);
}
if (tymin > tmin)
{
tmin = tymin;
}
if (tymax < tmax)
{
tmax = tymax;
}
// z-dir
float tzmin = (-apothem - p.z) / d.z;
float tzmax = (apothem - p.z) / d.z;
if (tzmin > tzmax)
{
std::swap(tzmin, tzmax);
}
if ((tmin > tzmax) || (tzmin > tmax))
{ // no hit
return glm::vec4(0.f);
}
if (tzmin > tmin)
{
tmin = tzmin;
}
if (tzmax < tmax)
{
tmax = tzmax;
}
if (tmin <= 0 && tmax <= 0) // both behind camera
{
return glm::vec4(0.f);
} else if (tmin > 0) // tmin in front of camera
{
return p + tmin*d;
} else if (tmin <= 0) // tmax in front of camera
{
return p + tmax*d;
}
return glm::vec4(0.f);
}
/**
* @brief Finds the intersection point of a ray and a shape.
* The ray and shape should be in the same space for this function to work properly.
* This function does not check if the intersection point is in front of the camera.
* @param p, the point of the ray
* @param d, the direction of the space
* @param shape, the shape to be intersected with the ray
* @return the intersection point as a vec4. If there exists no intersection, returns vec4(0.f).
*/
glm::vec4 RayTracer::findIntersection(
glm::vec4 p,
glm::vec4 d,
const RenderShapeData& shape)
{
switch(shape.primitive.type) {
case PrimitiveType::PRIMITIVE_SPHERE:
return intersectCircle(p, d, shape);
case PrimitiveType::PRIMITIVE_CONE:
return intersectCone(p, d, shape);
case PrimitiveType::PRIMITIVE_CYLINDER:
return intersectCylinder(p, d, shape);
case PrimitiveType::PRIMITIVE_CUBE:
return intersectCube(p, d, shape);
case PrimitiveType::PRIMITIVE_MESH:
break;
}
return glm::vec4(0.f);
}
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