assimp/code/PolyTools.h

/*
Open Asset Import Library (ASSIMP)
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*/

/** @file PolyTools.h, various utilities for our dealings with arbitrary polygons */

#ifndef AI_POLYTOOLS_H_INCLUDED
#define AI_POLYTOOLS_H_INCLUDED

namespace Assimp {

// -------------------------------------------------------------------------------
/** Compute the signed area of a triangle.
 *  The function accepts an unconstrained template parameter for use with
 *  both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
template <typename T>
inline double GetArea2D(const T& v1, const T& v2, const T& v3) 
{
	return 0.5 * (v1.x * ((double)v3.y - v2.y) + v2.x * ((double)v1.y - v3.y) + v3.x * ((double)v2.y - v1.y));
}

// -------------------------------------------------------------------------------
/** Test if a given point p2 is on the left side of the line formed by p0-p1.
 *  The function accepts an unconstrained template parameter for use with
 *  both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
template <typename T>
inline bool OnLeftSideOfLine2D(const T& p0, const T& p1,const T& p2)
{
	return GetArea2D(p0,p2,p1) > 0;
}

// -------------------------------------------------------------------------------
/** Test if a given point is inside a given triangle in R2.
 * The function accepts an unconstrained template parameter for use with
 *  both aiVector3D and aiVector2D, but generally ignores the third coordinate.*/
template <typename T>
inline bool PointInTriangle2D(const T& p0, const T& p1,const T& p2, const T& pp)
{
	// Point in triangle test using baryzentric coordinates
	const aiVector2D v0 = p1 - p0;
	const aiVector2D v1 = p2 - p0;
	const aiVector2D v2 = pp - p0;

	double dot00 = v0 * v0;
	double dot01 = v0 * v1;
	double dot02 = v0 * v2;
	double dot11 = v1 * v1;
	double dot12 = v1 * v2;

	const double invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
	dot11 = (dot11 * dot02 - dot01 * dot12) * invDenom;
	dot00 = (dot00 * dot12 - dot01 * dot02) * invDenom;

	return (dot11 > 0) && (dot00 > 0) && (dot11 + dot00 < 1);
}


// -------------------------------------------------------------------------------
/** Check whether the winding order of a given polygon is counter-clockwise.
 *  The function accepts an unconstrained template parameter, but is intended 
 *  to be used only with aiVector2D and aiVector3D (z axis is ignored, only
 *  x and y are taken into account).
 * @note Code taken from http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/97/Ian/applet1.html and translated to C++
 */
template <typename T>
inline bool IsCCW(T* in, size_t npoints) {
	double aa, bb, cc, b, c, theta;
	double convex_turn;
	double convex_sum = 0;

	for (int i = 0; i < npoints - 2; i++) {
		aa = ((in[i+2].x - in[i].x) * (in[i+2].x - in[i].x)) +
			((-in[i+2].y + in[i].y) * (-in[i+2].y + in[i].y));

		bb = ((in[i+1].x - in[i].x) * (in[i+1].x - in[i].x)) +
			((-in[i+1].y + in[i].y) * (-in[i+1].y + in[i].y));

		cc = ((in[i+2].x - in[i+1].x) * 
			(in[i+2].x - in[i+1].x)) +
			((-in[i+2].y + in[i+1].y) *
			(-in[i+2].y + in[i+1].y));

		b = sqrt(bb);
		c = sqrt(cc);
		theta = acos((bb + cc - aa) / (2 * b * c));

		if (OnLeftSideOfLine2D(in[i],in[i+2],in[i+1])) {
			//	if (convex(in[i].x, in[i].y,
			//		in[i+1].x, in[i+1].y,
			//		in[i+2].x, in[i+2].y)) {
			convex_turn = AI_MATH_PI_F - theta;
			convex_sum += convex_turn;
		}
		else {
			convex_sum -= AI_MATH_PI_F - theta;
		}
	}
	aa = ((in[1].x - in[npoints-2].x) * 
		(in[1].x - in[npoints-2].x)) +
		((-in[1].y + in[npoints-2].y) * 
		(-in[1].y + in[npoints-2].y));

	bb = ((in[0].x - in[npoints-2].x) * 
		(in[0].x - in[npoints-2].x)) +
		((-in[0].y + in[npoints-2].y) * 
		(-in[0].y + in[npoints-2].y));

	cc = ((in[1].x - in[0].x) * (in[1].x - in[0].x)) +
		((-in[1].y + in[0].y) * (-in[1].y + in[0].y));

	b = sqrt(bb);
	c = sqrt(cc);
	theta = acos((bb + cc - aa) / (2 * b * c));

	//if (convex(in[npoints-2].x, in[npoints-2].y,
	//	in[0].x, in[0].y,
	//	in[1].x, in[1].y)) {
	if (OnLeftSideOfLine2D(in[npoints-2],in[1],in[0])) {
		convex_turn = AI_MATH_PI_F - theta;
		convex_sum += convex_turn;
	}
	else { 
		convex_sum -= AI_MATH_PI_F - theta;
	}

	return convex_sum >= (2 * AI_MATH_PI_F);
}


// -------------------------------------------------------------------------------
/** Compute the normal of an arbitrary polygon in R3.
 *
 *  The code is based on Newell's formula, that is a polygons normal is the ratio
 *  of its area when projected onto the three coordinate axes.
 *
 *  @param out Receives the output normal
 *  @param num Number of input vertices
 *  @param x X data source. x[ofs_x*n] is the n'th element. 
 *  @param y Y data source. y[ofs_y*n] is the y'th element 
 *  @param z Z data source. z[ofs_z*n] is the z'th element 
 *
 *  @note The data arrays must have storage for at least num+2 elements. Using
 *  this method is much faster than the 'other' NewellNormal()
 */
template <int ofs_x, int ofs_y, int ofs_z>
inline void NewellNormal (aiVector3D& out, int num, float* x, float* y, float* z)
{
	// Duplicate the first two vertices at the end
	x[(num+0)*ofs_x] = x[0]; 
	x[(num+1)*ofs_x] = x[ofs_x]; 

	y[(num+0)*ofs_y] = y[0]; 
	y[(num+1)*ofs_y] = y[ofs_y]; 

	z[(num+0)*ofs_z] = z[0]; 
	z[(num+1)*ofs_z] = z[ofs_z]; 

	float sum_xy = 0.0, sum_yz = 0.0, sum_zx = 0.0;

	float *xptr = x +ofs_x, *xlow = x, *xhigh = x + ofs_x*2;
	float *yptr = y +ofs_y, *ylow = y, *yhigh = y + ofs_y*2;
	float *zptr = z +ofs_z, *zlow = z, *zhigh = z + ofs_z*2;

	for (int tmp=0; tmp < num; tmp++) {
		sum_xy += (*xptr) * ( (*yhigh) - (*ylow) );
		sum_yz += (*yptr) * ( (*zhigh) - (*zlow) );
		sum_zx += (*zptr) * ( (*xhigh) - (*xlow) );

		xptr  += ofs_x;
		xlow  += ofs_x;
		xhigh += ofs_x;

		yptr  += ofs_y;
		ylow  += ofs_y;
		yhigh += ofs_y;

		zptr  += ofs_z;
		zlow  += ofs_z;
		zhigh += ofs_z;
	}
	out = aiVector3D(sum_yz,sum_zx,sum_xy);
}

} // ! Assimp

#endif