Added degenerate versions of ray/line-quad intersect

glm/gtx/intersect.hpp

@@ -140,6 +140,42 @@ namespace glm
 
 	);
 
+	//! Compute the intersection of a ray and any quadrilateral.
+	//! From the GLM_GTX_intersect extension
+	template <typename genType>
+	GLM_FUNC_DECL bool intersectRayDegenerateQuad(
+		genType const & orig, genType const & dir, 
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01,
+		genType & bilinearCoordinates
+	);
+
+	//! Compute the intersection of a ray and any quadrilateral.
+	//! Does not compute the bilinear coordinates of the intersection.
+	//! From the GLM_GTX_intersect extension
+	template<typename genType>
+	GLM_FUNC_DECL bool fastIntersectRayDegenerateQuad(
+		genType const & orig, genType const & dir,
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01
+	);
+
+	//! Compute the intersection of a line and any quadrilateral.
+	//! From the GLM_GTX_intersect extension
+	template<typename genType>
+	GLM_FUNC_DECL bool intersectLineDegenerateQuad(
+		genType const & orig, genType const & dir, 
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01,
+		genType & bilinearCoordinates
+	);
+
+	//! Compute the intersection of a line and any quadrilateral.
+	//! Does not compute the bilinear coordinates of the intersection.
+	//! From the GLM_GTX_intersect extension
+	template<typename genType>
+	GLM_FUNC_DECL bool fastIntersectLineDegenerateQuad(
+		genType const & orig, genType const & dir,
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01
+	);
+
 	/// @}
 }//namespace glm
 

glm/gtx/intersect.inl

@@ -449,7 +449,7 @@ namespace glm
 
 		return true;
 	}
-	
+
 	template<typename genType>
 	GLM_FUNC_QUALIFIER bool intersectLineQuad
 	(
@@ -676,5 +676,484 @@ namespace glm
 		return true;
 	}
 
+	template<typename genType>
+	GLM_FUNC_QUALIFIER bool intersectLineQuad
+	(
+		genType const & orig, genType const & dir, 
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01,
+		genType & bilinearCoordinates
+	)
+	{
+		// Epsilon to reject parallell lines
+		typename genType::value_type epsilon = std::numeric_limits<typename genType::value_type>::epsilon();
+
+		// Calculate edges and normal of first triangle
+		genType e01 = v10 - v00;
+		genType e03 = v01 - v00;
+
+		genType p = glm::cross(dir, e03);
+
+		typename genType::value_type det = glm::dot(e01, p);
+
+		// Reject rays orthagonal to the normal vector. I.e. rays parallell to the plane.
+		if(det < epsilon && det > -epsilon)
+			return false;
+
+		typename genType::value_type inv_det = typename genType::value_type(1.0f)/det;
+
+		genType s = orig - v00;
+
+		// Calculate the barycentric alpha coordinate of the first triangle
+		typename genType::value_type alpha = inv_det * glm::dot(s, p);
+
+		// It lies outside the triangle
+		if(alpha > typename genType::value_type(1.0f))
+			return false;
+
+		if(alpha < typename genType::value_type(0.0f))
+			return false;
+
+		// Vector perpendicular to T and e01 
+		genType q = glm::cross(s, e01);
+
+		// Calculate barycentric beta coordinate of the first triangle
+		typename genType::value_type beta = inv_det * glm::dot(dir, q);
+
+		if(beta > typename genType::value_type(1.0f))
+			return false;
+		if(beta < typename genType::value_type(0.0f))
+			return false;
+
+		bilinearCoordinates.z = inv_det * glm::dot(e03, q);
+
+		if(alpha + beta > typename genType::value_type(1.0f)){
+		// Do exactly the same for the second triangle
+
+			genType e23 = v01 - v11;
+			genType e21 = v10 - v11;
+
+			p = glm::cross(dir, e21);
+			
+			det = glm::dot(e23, p);
+
+			if(det < epsilon && det > -epsilon)
+				return false;
+
+			inv_det = typename genType::value_type(1.0f)/det;
+			s = orig - v11;
+
+			alpha = inv_det * glm::dot(s, p);
+
+			if(alpha < typename genType::value_type(0.0f))
+				return false;
+
+			q = glm::cross(s, e23);
+			beta = inv_det * glm::dot(dir, q);
+
+			if(beta < typename genType::value_type(0.0f))
+				return false;
+
+			// This to support degenerate squares
+			if(beta + alpha > typename genType::value_type(1.0f))
+				return false;
+			
+			bilinearCoordinates.z = inv_det * glm::dot(e21, q);
+		}
+
+		// Compute barycentric coordinates of v11
+		genType e02 = v11 - v00;
+		genType N = glm::cross(e01, e03);
+		
+		typename genType::value_type alpha_11, beta_11;
+
+		if(abs(N.x) >= abs(N.y) && abs(N.x) >= abs(N.z)) {
+			alpha_11 = (e02.y * e03.z - e02.z * e03.y) / N.x;
+			beta_11  = (e01.y * e02.z - e01.z * e02.y) / N.x;
+		} else if(abs(N.y) >= abs(N.x) && abs(N.y) >= abs(N.z)) {		
+			alpha_11 = (e02.z * e03.x - e02.x * e03.z) / N.x;
+			beta_11  = (e01.z * e02.x - e01.x * e02.z) / N.x;
+		} else {
+			alpha_11 = (e02.x * e03.y - e02.y * e03.x) / N.z;
+			beta_11  = (e01.x * e02.y - e01.y * e02.x) / N.z;
+		}
+
+		// Compute bilinear coordinates of the intersection point
+		if(abs(alpha_11 - typename genType::value_type(1.0f)) < epsilon) { 
+			bilinearCoordinates.x = alpha;
+			
+			if(abs(beta_11 - typename genType::value_type(1.0f)) < epsilon){
+				bilinearCoordinates.y = beta;
+			} else {
+				bilinearCoordinates.y = beta/(bilinearCoordinates.x * (beta_11 - typename genType::value_type(1.0f)) + typename genType::value_type(1.0f));
+			}
+
+		} else if(abs(beta_11 - typename genType::value_type(1.0f)) < epsilon) {
+			bilinearCoordinates.y = alpha;
+			bilinearCoordinates.x = alpha/(bilinearCoordinates.y*(alpha_11 - typename genType::value_type(1.0f)) + typename genType::value_type(1.0f));
+		} else {
+			typename genType::value_type a, b, c, discr, q;
+
+			a = -(beta_11 - typename genType::value_type(1.0f));
+			b = alpha*(beta_11 - 1) - beta*(alpha_11 - typename genType::value_type(1.0f)) - typename genType::value_type(1.0f);
+			c = alpha;
+
+			discr = b*b - typename genType::value_type(4.0f)*a*c;
+
+			// Get sign of b
+			typename genType::value_type sign = (typename genType::value_type(0) < b) - (b < typename genType::value_type(0));
+			
+			q = -(typename genType::value_type(0.5f)) * (b + sign*glm::fastSqrt(discr));
+
+			bilinearCoordinates.x = q/a;
+
+			if(bilinearCoordinates.x < 0 || bilinearCoordinates.y > 1){
+				bilinearCoordinates.x = c/q;
+			} 
+
+			bilinearCoordinates.y = beta/(bilinearCoordinates.x*(beta_11 - 1) + 1);
+		}
+
+		return true;
+	}
+
+	template<typename genType>
+	GLM_FUNC_QUALIFIER bool fastIntersectLineQuad
+	(
+		genType const & orig, genType const & dir,
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01
+
+	)
+	{
+		// Epsilon to reject parallell lines
+		typename genType::value_type epsilon = std::numeric_limits<typename genType::value_type>::epsilon();
+
+		// Calculate edges and normal of first triangle
+		genType e01 = v10 - v00;
+		genType e03 = v01 - v00;
+
+		genType p = glm::cross(dir, e03);
+
+		typename genType::value_type det = glm::dot(e01, p);
+
+		// Reject rays orthagonal to the normal vector. I.e. rays parallell to the plane.
+		if(det < epsilon && det > -epsilon)
+			return false;
+
+		typename genType::value_type inv_det = typename genType::value_type(1.0f)/det;
+
+
+		genType s = orig - v00;
+
+		// Calculate the barycentric alpha coordinate of the first triangle
+		typename genType::value_type alpha = inv_det * glm::dot(s, p);
+
+		// It lies outside the triangle
+		if(alpha > typename genType::value_type(1.0f))
+			return false;
+
+		if(alpha < typename genType::value_type(0.0f))
+			return false;
+
+		// Vector perpendicular to T and e01 
+		genType q = glm::cross(s, e01);
+
+		// Calculate barycentric beta coordinate of the first triangle
+		typename genType::value_type beta = inv_det * glm::dot(dir, q);
+
+		if(beta > typename genType::value_type(1.0f))
+			return false;
+		if(beta < typename genType::value_type(0.0f))
+			return false;
+
+
+		if(alpha + beta > typename genType::value_type(1.0f)){
+		// Do exactly the same for the second triangle
+
+			genType e23 = v01 - v11;
+			genType e21 = v10 - v11;
+
+			p = glm::cross(dir, e21);
+			
+			det = glm::dot(e23, p);
+
+			if(det < epsilon && det > -epsilon)
+				return false;
+
+			inv_det = typename genType::value_type(1.0f)/det;
+			s = orig - v11;
+
+			alpha = inv_det * glm::dot(s, p);
+
+			if(alpha < typename genType::value_type(0.0f))
+				return false;
+
+			q = glm::cross(s, e23);
+			beta = inv_det * glm::dot(dir, q);
+
+			if(beta < typename genType::value_type(0.0f))
+				return false;
+
+			// This to support degenerate squares
+			if(beta + alpha > typename genType::value_type(1.0f))
+				return false;
+			
+		}
+		
+		return true;
+	}
+
+	template<typename genType>
+	GLM_FUNC_QUALIFIER bool intersectLineDegenerateQuad
+	(
+		genType const & orig, genType const & dir, 
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01,
+		genType & bilinearCoordinates
+	)
+	{
+		genType e01, e03, p, s, q;
+		typename genType::value_type epsilon, det, inv_det, alpha, beta;
+		bool isInOne = true;
+
+		// Epsilon to reject parallell lines
+		epsilon = std::numeric_limits<typename genType::value_type>::epsilon();
+
+		// Calculate edges and normal of first triangle
+		e01 = v10 - v00;
+		e03 = v01 - v00;
+
+		p = glm::cross(dir, e03);
+
+		det = glm::dot(e01, p);
+
+		// Reject rays orthagonal to the normal vector. I.e. rays parallell to the plane.
+		if(det < epsilon && det > -epsilon){
+			isInOne = false;
+			goto second;	
+		}
+
+		inv_det = typename genType::value_type(1.0f)/det;
+		s = orig - v00;
+
+		// Calculate the barycentric alpha coordinate of the first triangle
+		alpha = inv_det * glm::dot(s, p);
+
+		// It lies outside the triangle
+		if(alpha > typename genType::value_type(1.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		if(alpha < typename genType::value_type(0.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		// Vector perpendicular to T and e01 
+		q = glm::cross(s, e01);
+
+		// Calculate barycentric beta coordinate of the first triangle
+		beta = inv_det * glm::dot(dir, q);
+
+		if(beta > typename genType::value_type(1.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		if(beta < typename genType::value_type(0.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		/* Intersection is not in the first triangle, check the second*/
+		second:
+		if(!isInOne || alpha + beta > typename genType::value_type(1.0f)){
+			// Do exactly the same for the second triangle
+
+			genType e23 = v01 - v11;
+			genType e21 = v10 - v11;
+
+			p = glm::cross(dir, e21);
+			
+			det = glm::dot(e23, p);
+
+			if(det < epsilon && det > -epsilon){
+				return false;
+			}
+
+			inv_det = typename genType::value_type(1.0f)/det;
+			s = orig - v11;
+
+			alpha = inv_det * glm::dot(s, p);
+
+			if(alpha < typename genType::value_type(0.0f))
+				return false;
+
+			q = glm::cross(s, e23);
+			beta = inv_det * glm::dot(dir, q);
+
+			if(beta < typename genType::value_type(0.0f))
+				return false;
+
+			// This to support degenerate squares
+			if(beta + alpha > typename genType::value_type(1.0f))
+				return false;
+		}
+		
+
+		// Compute barycentric coordinates of v11
+		genType e02 = v11 - v00;
+		genType N = glm::cross(e01, e03);
+		
+		typename genType::value_type alpha_11, beta_11;
+
+		if(abs(N.x) >= abs(N.y) && abs(N.x) >= abs(N.z)) {
+			alpha_11 = (e02.y * e03.z - e02.z * e03.y) / N.x;
+			beta_11  = (e01.y * e02.z - e01.z * e02.y) / N.x;
+		} else if(abs(N.y) >= abs(N.x) && abs(N.y) >= abs(N.z)) {		
+			alpha_11 = (e02.z * e03.x - e02.x * e03.z) / N.x;
+			beta_11  = (e01.z * e02.x - e01.x * e02.z) / N.x;
+		} else {
+			alpha_11 = (e02.x * e03.y - e02.y * e03.x) / N.z;
+			beta_11  = (e01.x * e02.y - e01.y * e02.x) / N.z;
+		}
+
+		// Compute bilinear coordinates of the intersection point
+		if(abs(alpha_11 - typename genType::value_type(1.0f)) < epsilon) { 
+			bilinearCoordinates.x = alpha;
+			
+			if(abs(beta_11 - typename genType::value_type(1.0f)) < epsilon){
+				bilinearCoordinates.y = beta;
+			} else {
+				bilinearCoordinates.y = beta/(bilinearCoordinates.x * (beta_11 - typename genType::value_type(1.0f)) + typename genType::value_type(1.0f));
+			}
+
+		} else if(abs(beta_11 - typename genType::value_type(1.0f)) < epsilon) {
+			bilinearCoordinates.y = alpha;
+			bilinearCoordinates.x = alpha/(bilinearCoordinates.y*(alpha_11 - typename genType::value_type(1.0f)) + typename genType::value_type(1.0f));
+		} else {
+			typename genType::value_type a, b, c, discr, q;
+
+			a = -(beta_11 - typename genType::value_type(1.0f));
+			b = alpha*(beta_11 - 1) - beta*(alpha_11 - typename genType::value_type(1.0f)) - typename genType::value_type(1.0f);
+			c = alpha;
+
+			discr = b*b - typename genType::value_type(4.0f)*a*c;
+
+			// Get sign of b
+			typename genType::value_type sign = (typename genType::value_type(0) < b) - (b < typename genType::value_type(0));
+			
+			q = -(typename genType::value_type(0.5f)) * (b + sign*glm::fastSqrt(discr));
+
+			bilinearCoordinates.x = q/a;
+
+			if(bilinearCoordinates.x < 0 || bilinearCoordinates.y > 1){
+				bilinearCoordinates.x = c/q;
+			} 
+
+			bilinearCoordinates.y = beta/(bilinearCoordinates.x*(beta_11 - 1) + 1);
+		}
+
+		return true;
+	}
+
+	template<typename genType>
+	GLM_FUNC_QUALIFIER bool fastIntersectLineDegenerateQuad
+	(
+		genType const & orig, genType const & dir,
+		genType const & v00, genType const & v10, genType const & v11, genType const & v01
+	)
+	{
+		genType e01, e03, p, s, q;
+		typename genType::value_type epsilon, det, inv_det, alpha, beta;
+		bool isInOne = true;
+
+		// Epsilon to reject parallell lines
+		epsilon = std::numeric_limits<typename genType::value_type>::epsilon();
+
+		// Calculate edges and normal of first triangle
+		e01 = v10 - v00;
+		e03 = v01 - v00;
+
+		p = glm::cross(dir, e03);
+
+		det = glm::dot(e01, p);
+
+		// Reject rays orthagonal to the normal vector. I.e. rays parallell to the plane.
+		if(det < epsilon && det > -epsilon){
+			isInOne = false;
+			goto second;	
+		}
+
+		inv_det = typename genType::value_type(1.0f)/det;
+		s = orig - v00;
+
+		// Calculate the barycentric alpha coordinate of the first triangle
+		alpha = inv_det * glm::dot(s, p);
+
+		// It lies outside the triangle
+		if(alpha > typename genType::value_type(1.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		if(alpha < typename genType::value_type(0.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		// Vector perpendicular to T and e01 
+		q = glm::cross(s, e01);
+
+		// Calculate barycentric beta coordinate of the first triangle
+		beta = inv_det * glm::dot(dir, q);
+
+		if(beta > typename genType::value_type(1.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		if(beta < typename genType::value_type(0.0f)){
+			isInOne = false;
+			goto second;
+		}
+
+		/* Intersection is not in the first triangle, check the second*/
+		second:
+		if(!isInOne || alpha + beta > typename genType::value_type(1.0f)){
+			// Do exactly the same for the second triangle
+
+			genType e23 = v01 - v11;
+			genType e21 = v10 - v11;
+
+			p = glm::cross(dir, e21);
+			
+			det = glm::dot(e23, p);
+
+			if(det < epsilon && det > -epsilon){
+				return false;
+			}
+
+			inv_det = typename genType::value_type(1.0f)/det;
+			s = orig - v11;
+
+			alpha = inv_det * glm::dot(s, p);
+
+			if(alpha < typename genType::value_type(0.0f))
+				return false;
+
+			q = glm::cross(s, e23);
+			beta = inv_det * glm::dot(dir, q);
+
+			if(beta < typename genType::value_type(0.0f))
+				return false;
+
+			// This to support degenerate squares
+			if(beta + alpha > typename genType::value_type(1.0f))
+				return false;
+		}
+		
+		return true;
+	}
+
 
 }//namespace glm