Added functions to determine point on a given surface.

GetClosestPointOnQuadricSurface() is the one.

cmath3d/TriangleMesh.cpp

@@ -513,3 +513,92 @@ int ActiveMesh::CalcQuadricSurface_Taubin(const int vertexID,
 
 	return 0;
 }
+
+
+bool ActiveMesh::GetPointOnQuadricSurface(const float x,const float y,
+                                          float &z1, float &z2,
+                                          const float (&coeffs)[10])
+{
+	const float a=coeffs[9];
+	const float b=coeffs[3] +coeffs[5]*x +coeffs[6]*y;
+	const float c=coeffs[0] +coeffs[1]*x +coeffs[2]*y
+	             +coeffs[4]*x*y +coeffs[7]*x*x +coeffs[8]*y*y;
+
+	const float sqArg=b*b - 4*a*c;
+	if (sqArg < 0.f) return false;
+
+	z1=(-b + sqrtf(sqArg)) / (2.f*a);
+	z2=(-b - sqrtf(sqArg)) / (2.f*a);
+
+	return true;
+}
+
+
+float ActiveMesh::GetClosestPointOnQuadricSurface(Vector3F& point,
+                                                  const float (&coeffs)[10])
+{
+	//backup original input coordinate
+	const float x=point.x;
+	const float y=point.y;
+	const float z=point.z;
+	float tmp1,tmp2;
+
+	//list of possible coordinates
+	std::vector<Vector3F> pointAdepts;
+
+	//took a pair of coordinates, calculate the third one
+	//and make it an adept...
+	if (GetPointOnQuadricSurface(x,y,tmp1,tmp2,coeffs))
+	{
+		pointAdepts.push_back(Vector3F(x,y,tmp1));
+		pointAdepts.push_back(Vector3F(x,y,tmp2));
+	}
+	if (GetPointOnQuadricSurface(x,z,tmp1,tmp2,coeffs))
+	{
+		pointAdepts.push_back(Vector3F(x,tmp1,z));
+		pointAdepts.push_back(Vector3F(x,tmp2,z));
+	}
+	if (GetPointOnQuadricSurface(y,z,tmp1,tmp2,coeffs))
+	{
+		pointAdepts.push_back(Vector3F(tmp1,y,z));
+		pointAdepts.push_back(Vector3F(tmp2,y,z));
+	}
+
+	//are we doomed?
+	if (pointAdepts.size() == 0)
+		return (-999999.f);
+
+	//find the closest
+	int closestIndex=ChooseClosestPoint(pointAdepts,point);
+	
+	//calc distance to it
+	point-=pointAdepts[closestIndex];
+	tmp1=point.Len();
+
+	//adjust the input/output point
+	point=pointAdepts[closestIndex];
+
+	return (tmp1);
+}
+
+
+int ActiveMesh::ChooseClosestPoint(const std::vector<Vector3F>& points,
+                                   const Vector3F& point)
+{
+	int minIndex=-1;
+	float minSqDist=9999999999999.f;
+
+	Vector3F p;
+	for (unsigned int i=0; i < points.size(); ++i)
+	{
+		p=point;
+		p-=points[i];
+		if (p.LenQ() < minSqDist)
+		{
+			minIndex=i;
+			minSqDist=p.LenQ();
+		}
+	}
+
+	return minIndex;
+}

cmath3d/TriangleMesh.h

@@ -33,15 +33,47 @@ class ActiveMesh
 	 * Scalar product of \e coeffs and [1,x,y,z,xy,xz,yz,x^2,y^2,z^2] = 0.
 	 * This also explains the order (and meaning) of the \e coeffs array.
 	 * Order was adopted from [1], eq (2), page 3.
-	 * 
+	 *
+	 * The algorithm has been implemented according to
+	 * the "instructions" [2], Appendix A, page 131.
 	 * 
 	 * [1]: Dong-Ming Yan, Wenping Wang, Yang Liu, Zhouwang Yang.
 	 * Variational mesh segmentation via quadric surface fitting.
 	 * Elsevier: Computer-Aided Design 44 (2012), pp. 1072-1082.
+	 *
+	 * [2]: Hui Ma, Geometric Fitting of Quadratic Curves and Surfaces,
+	 * Dissertation Thesis, Univ. Alabama, 2011.
 	 */
 	int CalcQuadricSurface_Taubin(const int vertexID,
 	                              float (&coeffs)[10]);
 
+	/**
+	 * Calculate the 3rd coordinate (e.g., z) to complete a 3D point
+	 * [x,y,z] given the other two coordinates (e.g., x and y).
+	 * The point should lay on the quadric surface given with
+	 * the coefficients \e coeffs.
+	 *
+	 * Returns false if such point could not be determined.
+	 *
+	 * Note that due to symmetries in the equations, one can use
+	 * the very same function to obtain x given y,z, etc.
+	 *
+	 * Also note that two points are actually generated, one need
+	 * to examine their distance to the point around which the surface
+	 * has been calculated, and take the closer one.
+	 */
+	bool GetPointOnQuadricSurface(const float x,const float y,
+	                              float &z1, float &z2,
+	                              const float (&coeffs)[10]);
+
+	///Adjusts the input \e point to arrive at the surface given by its \e coeffs,
+	///the value of \e point is, therefore, changed.
+	float GetClosestPointOnQuadricSurface(Vector3F& point,
+	                                      const float (&coeffs)[10]);
+
+	///returns index of the closest from \e points to the \e point
+	int ChooseClosestPoint(const std::vector<Vector3F>& points,
+	                       const Vector3F& point);
 
 
 	///input is filename
@@ -54,7 +86,10 @@ class ActiveMesh
 	void CenterMesh(const Vector3F& newCentre);
 	void ScaleMesh(const Vector3F& scale);
 
-	void displayMesh(void); //defined in graphics.cpp
+	//the following functions are all defined in graphics.cpp
+	void displayMesh(void);
+	void displayVertexAndNeigs(void);
+	void displayQuadricSurface(void);
 };
 
 #endif