void CSprite::drawCentered()
{
draw(_x - getHalfWidth(), _y - getHalfHeight());
}
bool CapsuleShape::findRayIntersection(RayIntersectionInfo& intersection) const {
// ray is U, capsule is V
glm::vec3 axisV;
computeNormalizedAxis(axisV);
glm::vec3 centerV = getTranslation();
// first handle parallel case
float uDotV = glm::dot(axisV, intersection._rayDirection);
glm::vec3 UV = intersection._rayStart - centerV;
if (glm::abs(1.0f - glm::abs(uDotV)) < EPSILON) {
// line and cylinder are parallel
float distanceV = glm::dot(UV, intersection._rayDirection);
if (glm::length2(UV - distanceV * intersection._rayDirection) <= _radius * _radius) {
// ray is inside cylinder's radius and might intersect caps
return findRayIntersectionWithCaps(centerV, intersection);
}
return false;
}
// Given a line with point 'U' and normalized direction 'u' and
// a cylinder with axial point 'V', radius 'r', and normalized direction 'v'
// the intersection of the two is on the line at distance 't' from 'U'.
//
// Determining the values of t reduces to solving a quadratic equation: At^2 + Bt + C = 0
//
// where:
//
// UV = U-V
// w = u-(u.v)v
// Q = UV-(UV.v)v
//
// A = w^2
// B = 2(w.Q)
// C = Q^2 - r^2
glm::vec3 w = intersection._rayDirection - uDotV * axisV;
glm::vec3 Q = UV - glm::dot(UV, axisV) * axisV;
// we save a few multiplies by storing 2*A rather than just A
float A2 = 2.0f * glm::dot(w, w);
float B = 2.0f * glm::dot(w, Q);
// since C is only ever used once (in the determinant) we compute it inline
float determinant = B * B - 2.0f * A2 * (glm::dot(Q, Q) - _radius * _radius);
if (determinant < 0.0f) {
return false;
}
float hitLow = (-B - sqrtf(determinant)) / A2;
float hitHigh = -(hitLow + 2.0f * B / A2);
if (hitLow > hitHigh) {
// re-arrange so hitLow is always the smaller value
float temp = hitHigh;
hitHigh = hitLow;
hitLow = temp;
}
if (hitLow < 0.0f) {
if (hitHigh < 0.0f) {
// capsule is completely behind rayStart
return false;
}
hitLow = hitHigh;
}
glm::vec3 p = intersection._rayStart + hitLow * intersection._rayDirection;
float d = glm::dot(p - centerV, axisV);
if (glm::abs(d) <= getHalfHeight()) {
// we definitely hit the cylinder wall
intersection._hitDistance = hitLow;
intersection._hitNormal = glm::normalize(p - centerV - d * axisV);
intersection._hitShape = const_cast<CapsuleShape*>(this);
return true;
}
// ray still might hit the caps
return findRayIntersectionWithCaps(centerV, intersection);
}