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Correctly compute conical frustum for irregular ones

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Clement 2018-04-30 19:51:18 -07:00
parent 67c119cd2e
commit b4ea32bbb6
1 changed files with 11 additions and 25 deletions
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36
libraries/shared/src/shared/ConicalViewFrustum.cpp
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@ -17,38 +17,24 @@ void ConicalViewFrustum::set(const ViewFrustum& viewFrustum) {
// The ConicalViewFrustum has two parts: a central sphere (same as ViewFrustum) and a circular cone that bounds the frustum part. // The ConicalViewFrustum has two parts: a central sphere (same as ViewFrustum) and a circular cone that bounds the frustum part.
// Why? Because approximate intersection tests are much faster to compute for a cone than for a frustum. // Why? Because approximate intersection tests are much faster to compute for a cone than for a frustum.
_position = viewFrustum.getPosition(); _position = viewFrustum.getPosition();
_direction = viewFrustum.getDirection();
_radius = viewFrustum.getCenterRadius(); _radius = viewFrustum.getCenterRadius();
_farClip = viewFrustum.getFarClip(); _farClip = viewFrustum.getFarClip();
// Considering the rectangle intersection the frustum and the perpendicular plane 1 unit auto topLeft = viewFrustum.getNearTopLeft() - _position;
// away from the frustum's origin auto topRight = viewFrustum.getNearTopRight() - _position;
// We are looking for the angle between the ray that goes through the center of the rectangle auto bottomLeft = viewFrustum.getNearBottomLeft() - _position;
// and the ray that goes through one of the corners of the rectangle auto bottomRight = viewFrustum.getNearBottomRight() - _position;
// (Both rays coming from the frustum's origin) auto centerAxis = 0.25f * (topLeft + topRight + bottomLeft + bottomRight); // Take the average
// This angle will let us construct a cone in which the frustum is inscribed
// Let's define:
// A = aspect ratio = width / height
// fov = vertical field of view
// y = half height of the rectangle
// x = half width of the rectangle
// r = half diagonal of the rectangle
// then, we have:
// y / 1 = tan(fov / 2)
// x = A * y = A * tan(fov / 2)
// r^2 = x^2 + y^2 = (A^2 + 1) * tan^2(fov / 2)
// r / 1 = tan(angle) = sqrt((A^2 + 1) * tan^2(fov / 2))
// angle = atan(sqrt((A^2 + 1) * tan^2(fov / 2)))
float A = viewFrustum.getAspectRatio();
float t = tanf(0.5f * viewFrustum.getFieldOfView());
auto tan2Angle = (A * A + 1.0f) * (t * t); _direction = glm::normalize(centerAxis);
_angle = atanf(sqrt(tan2Angle)); _angle = std::max(std::max(angleBetween(_direction, topLeft),
angleBetween(_direction, topRight)),
calculate(); std::max(angleBetween(_direction, bottomLeft),
angleBetween(_direction, bottomRight)));
} }
void ConicalViewFrustum::calculate() { void ConicalViewFrustum::calculate() {
// Pre-compute cos and sin for faster checks
_cosAngle = cosf(_angle); _cosAngle = cosf(_angle);
_sinAngle = sqrtf(1.0f - _cosAngle * _cosAngle); _sinAngle = sqrtf(1.0f - _cosAngle * _cosAngle);
} }