GLUSvoid GLUSAPIENTRY glusVector3Refractf(GLUSfloat result[3], const GLUSfloat incident[3], const GLUSfloat normal[3], const float eta)
{
// see http://www.opengl.org/sdk/docs/manglsl/xhtml/refract.xml
// see http://en.wikipedia.org/wiki/Snell%27s_law
// see http://www.hugi.scene.org/online/coding/hugi%2023%20-%20torefrac.htm for a and b vector.
// In this implementation, the incident vector points into the interface. So the sings do change.
GLUSfloat nDotI = glusVector3Dotf(normal, incident);
GLUSfloat k = 1.0f - eta * eta * (1.0f - nDotI * nDotI);
if (k < 0.0f)
{
result[0] = 0.0f;
result[1] = 0.0f;
result[2] = 0.0f;
}
else
{
GLUSfloat a[3];
GLUSfloat b[3];
glusVector3MultiplyScalarf(a, incident, eta);
glusVector3MultiplyScalarf(b, normal, eta * nDotI + sqrtf(k));
glusVector3SubtractVector3f(result, a, b);
}
}
GLUSfloat GLUSAPIENTRY glusVector3Fresnelf(const GLUSfloat incident[3], const GLUSfloat normal[3], const GLUSfloat R0)
{
// see http://en.wikipedia.org/wiki/Schlick%27s_approximation
GLUSfloat negIncident[3];
glusVector3MultiplyScalarf(negIncident, incident, -1.0f);
return R0 + (1.0f - R0) * powf(1.0f - glusVector3Dotf(negIncident, normal), 5.0f);
}
GLUSboolean GLUSAPIENTRY glusVector3GramSchmidtOrthof(GLUSfloat result[3], const GLUSfloat u[3], const GLUSfloat v[3])
{
GLUSfloat uProjV[3];
GLUSfloat vDotU;
GLUSfloat uDotU = glusVector3Dotf(u, u);
if (uDotU == 0.0f)
{
return GLUS_FALSE;
}
vDotU = glusVector3Dotf(v, u);
uProjV[0] = u[0] * vDotU / uDotU;
uProjV[1] = u[1] * vDotU / uDotU;
uProjV[2] = u[2] * vDotU / uDotU;
glusVector3SubtractVector3f(result, v, uProjV);
return GLUS_TRUE;
}
GLUSvoid GLUSAPIENTRY glusPlaneCreatef(GLUSfloat result[4], const GLUSfloat point[4], const GLUSfloat normal[3])
{
GLUSfloat normalized[3];
glusVector3Copyf(normalized, normal);
glusVector3Normalizef(normalized);
result[0] = normalized[0];
result[1] = normalized[1];
result[2] = normalized[2];
// D = -N*P
result[3] = -glusVector3Dotf(normalized, point);
}
GLUSvoid GLUSAPIENTRY glusVector2Reflectf(GLUSfloat result[2], const GLUSfloat incident[2], const GLUSfloat normal[2])
{
glusVector2MultiplyScalarf(result, normal, 2.0f * glusVector3Dotf(normal, incident));
glusVector2SubtractVector2f(result, incident, result);
}
static GLvoid march(GLfloat pixelColor[4], const GLfloat rayPosition[4], const GLfloat rayDirection[3], const GLint depth)
{
GLint i, k, m, o;
Primitive* primitiveNear = 0;
GLfloat marchPosition[4];
GLfloat marchDirection[3];
GLfloat hitPosition[4];
GLfloat hitDirection[3];
GLfloat eyeDirection[3];
GLfloat t = 0.0f;
//
pixelColor[0] = 0.0f;
pixelColor[1] = 0.0f;
pixelColor[2] = 0.0f;
pixelColor[3] = 1.0f;
//
for (i = 0; i < MAX_STEPS; i++)
{
GLfloat distance = INFINITY;
GLfloat currentDistance;
Primitive* closestPrimitive = 0;
glusVector3MultiplyScalarf(marchDirection, rayDirection, t);
glusPoint4AddVector3f(marchPosition, rayPosition, marchDirection);
for (k = 0; k < NUM_SPHERES + NUM_BOXES; k++)
{
Primitive* currentPrimitive = &g_allPrimitives[k];
currentDistance = currentPrimitive->distanceFunction(marchPosition, currentPrimitive);
if (currentDistance < distance)
{
distance = currentDistance;
closestPrimitive = currentPrimitive;
}
}
if (distance < EPSILON)
{
GLfloat samplePoints[4 * 6];
// Copy hit position ...
glusPoint4Copyf(hitPosition, marchPosition);
// ... and calculate normal by sampling around the hit position.
for (k = 0; k < 6; k++)
{
samplePoints[k*4+0] = hitPosition[0];
samplePoints[k*4+1] = hitPosition[1];
samplePoints[k*4+2] = hitPosition[2];
samplePoints[k*4+3] = hitPosition[3];
samplePoints[k*4+k/2] += GAMMA * (k%2 == 0 ? 1.0f : -1.0f);
}
for (k = 0; k < 3; k++)
{
hitDirection[k] = closestPrimitive->distanceFunction(&samplePoints[k*2*4 + 0], closestPrimitive) - closestPrimitive->distanceFunction(&samplePoints[k*2*4 + 4], closestPrimitive);
}
glusVector3Normalizef(hitDirection);
primitiveNear = closestPrimitive;
break;
}
// If t is larger than a given distance, assume that there is the nothing.
if (t > MAX_DISTANCE)
{
break;
}
t += distance;
}
//
// No intersection, return background color / ambient light.
if (!primitiveNear)
{
pixelColor[0] = 0.8f;
pixelColor[1] = 0.8f;
pixelColor[2] = 0.8f;
return;
}
//
glusVector3MultiplyScalarf(eyeDirection, rayDirection, -1.0f);
// Diffuse and specular color
for (i = 0; i < NUM_LIGHTS; i++)
{
PointLight* pointLight = &g_allLights[i];
GLboolean obstacle = GL_FALSE;
GLfloat lightDirection[3];
GLfloat incidentLightDirection[3];
glusPoint4SubtractPoint4f(lightDirection, pointLight->position, hitPosition);
glusVector3Normalizef(lightDirection);
glusVector3MultiplyScalarf(incidentLightDirection, lightDirection, -1.0f);
// Check for obstacles between current hit point surface and point light.
for (k = 0; k < NUM_SPHERES + NUM_BOXES; k++)
{
Primitive* obstaclePrimitive = &g_allPrimitives[k];
if (obstaclePrimitive == primitiveNear)
{
continue;
}
t = 0.0f;
for (m = 0; m < MAX_STEPS; m++)
{
GLfloat distance = INFINITY;
GLfloat currentDistance;
Primitive* closestPrimitive = 0;
glusVector3MultiplyScalarf(marchDirection, lightDirection, -t);
glusPoint4AddVector3f(marchPosition, pointLight->position, marchDirection);
for (o = 0; o < NUM_SPHERES + NUM_BOXES; o++)
{
Primitive* currentPrimitive = &g_allPrimitives[o];
currentDistance = currentPrimitive->distanceFunction(marchPosition, currentPrimitive);
if (currentDistance < distance && currentDistance >= 0.0f)
{
distance = currentDistance;
closestPrimitive = currentPrimitive;
}
else if (currentDistance > distance && currentDistance < 0.0f)
{
distance = currentDistance;
closestPrimitive = currentPrimitive;
}
}
if (distance < EPSILON)
{
if (closestPrimitive != primitiveNear)
{
obstacle = GL_TRUE;
}
break;
}
if (t > MAX_DISTANCE)
{
break;
}
t += distance;
}
}
// If no obstacle, illuminate hit point surface.
if (!obstacle)
{
GLfloat diffuseIntensity = glusMathMaxf(0.0f, glusVector3Dotf(hitDirection, lightDirection));
if (diffuseIntensity > 0.0f)
{
GLfloat specularReflection[3];
GLfloat eDotR;
pixelColor[0] = pixelColor[0] + diffuseIntensity * primitiveNear->material.diffuseColor[0] * pointLight->color[0];
pixelColor[1] = pixelColor[1] + diffuseIntensity * primitiveNear->material.diffuseColor[1] * pointLight->color[1];
pixelColor[2] = pixelColor[2] + diffuseIntensity * primitiveNear->material.diffuseColor[2] * pointLight->color[2];
glusVector3Reflectf(specularReflection, incidentLightDirection, hitDirection);
glusVector3Normalizef(specularReflection);
eDotR = glusMathMaxf(0.0f, glusVector3Dotf(eyeDirection, specularReflection));
if (eDotR > 0.0f)
{
GLfloat specularIntensity = powf(eDotR, primitiveNear->material.shininess);
pixelColor[0] = pixelColor[0] + specularIntensity * primitiveNear->material.specularColor[0] * pointLight->color[0];
pixelColor[1] = pixelColor[1] + specularIntensity * primitiveNear->material.specularColor[1] * pointLight->color[1];
pixelColor[2] = pixelColor[2] + specularIntensity * primitiveNear->material.specularColor[2] * pointLight->color[2];
}
}
}
}
// Emissive color
pixelColor[0] = pixelColor[0] + primitiveNear->material.emissiveColor[0];
pixelColor[1] = pixelColor[1] + primitiveNear->material.emissiveColor[1];
pixelColor[2] = pixelColor[2] + primitiveNear->material.emissiveColor[2];
}
float Vector3::dot(const Vector3& other) const
{
return glusVector3Dotf(v, other.v);
}
GLUSfloat GLUSAPIENTRY glusPlaneDistancePoint4f(const GLUSfloat plane[4], const GLUSfloat point[4])
{
return glusVector3Dotf(plane, point) + plane[3];
}
static GLvoid trace(GLfloat pixelColor[4], const GLfloat rayPosition[4], const GLfloat rayDirection[3], const GLint depth)
{
const GLfloat bias = 1e-4f;
GLint i, k;
GLfloat tNear = INFINITY;
Sphere* sphereNear = 0;
GLboolean insideSphereNear = GL_FALSE;
GLfloat ray[3];
GLfloat hitPosition[4];
GLfloat hitDirection[3];
GLfloat biasedPositiveHitPosition[4];
GLfloat biasedNegativeHitPosition[4];
GLfloat biasedHitDirection[3];
GLfloat eyeDirection[3];
//
pixelColor[0] = 0.0f;
pixelColor[1] = 0.0f;
pixelColor[2] = 0.0f;
pixelColor[3] = 1.0f;
//
for (i = 0; i < NUM_SPHERES; i++)
{
GLfloat t0 = INFINITY;
GLfloat t1 = INFINITY;
GLboolean insideSphere = GL_FALSE;
Sphere* currentSphere = &g_allSpheres[i];
GLint numberIntersections = glusIntersectRaySpheref(&t0, &t1, &insideSphere, rayPosition, rayDirection, currentSphere->center, currentSphere->radius);
if (numberIntersections)
{
// If intersection happened inside the sphere, take second intersection point, as this one is on the surface.
if (insideSphere)
{
t0 = t1;
}
// Found a sphere, which is closer.
if (t0 < tNear)
{
tNear = t0;
sphereNear = currentSphere;
insideSphereNear = insideSphere;
}
}
}
//
// No intersection, return background color / ambient light.
if (!sphereNear)
{
pixelColor[0] = 0.8f;
pixelColor[1] = 0.8f;
pixelColor[2] = 0.8f;
return;
}
// Calculate ray hit position ...
glusVector3MultiplyScalarf(ray, rayDirection, tNear);
glusPoint4AddVector3f(hitPosition, rayPosition, ray);
// ... and normal
glusPoint4SubtractPoint4f(hitDirection, hitPosition, sphereNear->center);
glusVector3Normalizef(hitDirection);
// If inside the sphere, reverse hit vector, as ray comes from inside.
if (insideSphereNear)
{
glusVector3MultiplyScalarf(hitDirection, hitDirection, -1.0f);
}
//
// Biasing, to avoid artifacts.
glusVector3MultiplyScalarf(biasedHitDirection, hitDirection, bias);
glusPoint4AddVector3f(biasedPositiveHitPosition, hitPosition, biasedHitDirection);
glusPoint4SubtractVector3f(biasedNegativeHitPosition, hitPosition, biasedHitDirection);
//
GLfloat reflectionColor[4] = {0.0f, 0.0f, 0.0f, 1.0f};
GLfloat refractionColor[4] = {0.0f, 0.0f, 0.0f, 1.0f};
GLfloat fresnel = glusVector3Fresnelf(rayDirection, hitDirection, R0);
// Reflection ...
if (sphereNear->material.reflectivity > 0.0f && depth < MAX_RAY_DEPTH)
{
GLfloat reflectionDirection[3];
glusVector3Reflectf(reflectionDirection, rayDirection, hitDirection);
glusVector3Normalizef(reflectionDirection);
trace(reflectionColor, biasedPositiveHitPosition, reflectionDirection, depth + 1);
}
// ... refraction.
if (sphereNear->material.alpha < 1.0f && depth < MAX_RAY_DEPTH)
{
GLfloat refractionDirection[3];
// If inside, it is from glass to air.
GLfloat eta = insideSphereNear ? 1.0f / Eta : Eta;
glusVector3Refractf(refractionDirection, rayDirection, hitDirection, eta);
glusVector3Normalizef(refractionDirection);
trace(refractionColor, biasedNegativeHitPosition, refractionDirection, depth + 1);
}
else
{
fresnel = 1.0f;
}
//
glusVector3MultiplyScalarf(eyeDirection, rayDirection, -1.0f);
// Diffuse and specular color
for (i = 0; i < NUM_LIGHTS; i++)
{
PointLight* pointLight = &g_allLights[i];
GLboolean obstacle = GL_FALSE;
GLfloat lightDirection[3];
GLfloat incidentLightDirection[3];
glusPoint4SubtractPoint4f(lightDirection, pointLight->position, hitPosition);
glusVector3Normalizef(lightDirection);
glusVector3MultiplyScalarf(incidentLightDirection, lightDirection, -1.0f);
// Check for obstacles between current hit point surface and point light.
for (k = 0; k < NUM_SPHERES; k++)
{
Sphere* obstacleSphere = &g_allSpheres[k];
if (obstacleSphere == sphereNear)
{
continue;
}
if (glusIntersectRaySpheref(0, 0, 0, biasedPositiveHitPosition, lightDirection, obstacleSphere->center, obstacleSphere->radius))
{
obstacle = GL_TRUE;
break;
}
}
// If no obstacle, illuminate hit point surface.
if (!obstacle)
{
GLfloat diffuseIntensity = glusMaxf(0.0f, glusVector3Dotf(hitDirection, lightDirection));
if (diffuseIntensity > 0.0f)
{
GLfloat specularReflection[3];
GLfloat eDotR;
pixelColor[0] = pixelColor[0] + diffuseIntensity * sphereNear->material.diffuseColor[0] * pointLight->color[0];
pixelColor[1] = pixelColor[1] + diffuseIntensity * sphereNear->material.diffuseColor[1] * pointLight->color[1];
pixelColor[2] = pixelColor[2] + diffuseIntensity * sphereNear->material.diffuseColor[2] * pointLight->color[2];
glusVector3Reflectf(specularReflection, incidentLightDirection, hitDirection);
glusVector3Normalizef(specularReflection);
eDotR = glusMaxf(0.0f, glusVector3Dotf(eyeDirection, specularReflection));
if (eDotR > 0.0f && !insideSphereNear)
{
GLfloat specularIntensity = powf(eDotR, sphereNear->material.shininess);
pixelColor[0] = pixelColor[0] + specularIntensity * sphereNear->material.specularColor[0] * pointLight->color[0];
pixelColor[1] = pixelColor[1] + specularIntensity * sphereNear->material.specularColor[1] * pointLight->color[1];
pixelColor[2] = pixelColor[2] + specularIntensity * sphereNear->material.specularColor[2] * pointLight->color[2];
}
}
}
}
// Emissive color
pixelColor[0] = pixelColor[0] + sphereNear->material.emissiveColor[0];
pixelColor[1] = pixelColor[1] + sphereNear->material.emissiveColor[1];
pixelColor[2] = pixelColor[2] + sphereNear->material.emissiveColor[2];
// Final color with reflection and refraction
pixelColor[0] = (1.0f - fresnel) * refractionColor[0] * (1.0f - sphereNear->material.alpha) + pixelColor[0] * (1.0f - sphereNear->material.reflectivity) * sphereNear->material.alpha + fresnel * reflectionColor[0] * sphereNear->material.reflectivity;
pixelColor[1] = (1.0f - fresnel) * refractionColor[1] * (1.0f - sphereNear->material.alpha) + pixelColor[1] * (1.0f - sphereNear->material.reflectivity) * sphereNear->material.alpha + fresnel * reflectionColor[1] * sphereNear->material.reflectivity;
pixelColor[2] = (1.0f - fresnel) * refractionColor[2] * (1.0f - sphereNear->material.alpha) + pixelColor[2] * (1.0f - sphereNear->material.reflectivity) * sphereNear->material.alpha + fresnel * reflectionColor[2] * sphereNear->material.reflectivity;
}