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# Interpolation

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Hi, I need some help with intepolation. I have a triangle, which lies inside a bounding box (Actually a lightmap). Each vertex has a value and I need to find the interpolated value for the all pixels of the image. Any help? [image]http://jmb.mine.nu/~sunray/face.png[/image] [edited by - Sunray on August 17, 2003 5:19:58 PM]

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some code I use. Maybe there is a simpler solution that I don''t know of, so keep posting

//-------------------------------------------------------------------------// Compute the weighted averages.// ------------------------------////                        + A//                      e/ \//                      /   \//                   H +     \//                    /  .    \ //                   /     + P \//                  /        .  \//                 /          .  \ //                /            f. \//               /                .\//              +-------------------+//             B                     C//// triangle made of points A, B, C and normal D////// P is the point projected on the triangle plane (N, A).//// H is the intersection of ray (C, CP) with edge plane ((AB x N), A)//// then,// // AH = e.AB// CP = f.CH //// => H = A + e.AB// => P = C + f.CH//// => H  = e.A + (1 - e).B// => P  = f.H + (1 - f).C//// => P = ef(A) + (f - ef)(B) + (1 - f)(C)// // and e = 1.0f - |AH| / |AB|// and f = 1,0f - |CP| / |CH|//// => weight[0] = ef//    weight[1] = (f - ef)//    weight[2] = (1 - f)//-------------------------------------------------------------------------void ComputeWeights(const Vector& Point, const Vector& A, const Vector& B, const Vector& C, float* Weights){	//-------------------------------------------------------------------------	// compute Triangle Normal	//-------------------------------------------------------------------------	Vector E;	Vector F;	Vector N;	E = B; E -= A;	F = C; F -= B;	N.Cross(E, F);		//-------------------------------------------------------------------------	// project point on triangle plane	//-------------------------------------------------------------------------	Vector P; 	P = Point;	float d = P * N - (A * N);	P.AddScaledVector(-d, N);		Vector AB;	Vector ABxN;	Vector CP;	//-------------------------------------------------------------------------	// compute edge plane (AB x N, A)	//-------------------------------------------------------------------------	AB = B; AB -= A;	ABxN.Cross(AB, N);	//-------------------------------------------------------------------------	// compute intersection distance	//-------------------------------------------------------------------------	CP  = P; CP -= C;	float det = CP * ABxN;	if (FABS(det) < 0.000001f)	{		Weights[0] = 0.0f;		Weights[1] = 0.0f;		Weights[2] = 1.0f;		return;	}	float t = (ABxN * A - C * ABxN) / det;	//-------------------------------------------------------------------------	// compute intersection point	//-------------------------------------------------------------------------	//Vector H;	H = C;	H.AddScaledVector(t, CP);	//	float e;//	float f;	//-------------------------------------------------------------------------	// compute first interpolation factor on edge AB	//-------------------------------------------------------------------------	Vector AH;	AH = H; AH -= A;	float ab = AB.GetLength();	float ah = AH.GetLength();	e = (ah / ab);	//-------------------------------------------------------------------------	// compute second interpolation factor on segment CH	//-------------------------------------------------------------------------	Vector CH; 	CH = H; CH -= C;	float ch = CH.GetLength();	float cp = CP.GetLength();	if (ch < 0.00001f)	{		Weights[0] = 0.0f;		Weights[1] = 0.0f;		Weights[2] = 1.0f;		return;	}	f = (cp / ch);	//-------------------------------------------------------------------------	// compute the weights	//-------------------------------------------------------------------------	Weights[0] = f - e * f;	Weights[1] = e * f;	Weights[2] = 1.0f - f;}

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I am doing something very similar. In my case, I have a 2d triangle and each corner, has a height, I try to find the height at some point inside of the triangle...

For your situation, do it this way:
1) find a line that foes through the point you are trying to find and 2 edges of the tri
2) find where this new line intersects the triangle
3) you will have 2 intersection points between this line and your triangle; find the value of these points.
4) find the value of the piont by interpolating between the two intersection points

Basically you have 3 linear interpolations. This algorithm can be greatly simplified in most cases. As in my case, where all triangles are right triangles, I use the following code:

void Terrain::GetHeightAtPoint(D3DXVECTOR2 &vec2, float &height){	float xd = 1;	float yd = 1;	float z0 = 1;	float z1 = .5;	float z2 = 0;	float w  = (xd - ((xd - vec2.x) + (yd - vec2.y))) / xd;	float ah = z0 * (1 - w) + z2 * w;	float bh = z1 * (1 - w) + z2 * w;	height = (bh * (yd - vec2.y) + ah * (xd - vec2.x)) / ((yd - vec2.y) + (xd - vec2.x));}

in this case, for simplicity, jz0, z1, and z2 are the values you wish to interpolate

This is a little different than u were asking for, but should be close enough to get you going in the right direction

Hope I could help

Dwiel

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