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OpenGL Problem with Tangent and Bitangent calculation

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Hello, I want to do some normal mapping with OpenGL and GLSL. To do this I need a way to calculate the tangent space base vectors. I do this by using the code posted on Computing tangent space basis vectors for an arbitrary mesh By the way, my application uses right-handed coordinates. I wrote a simple test program to test the output of the tangent calculation function and there is a problem: I pass a single triangle in the X/Y plane with normal (1,0,0)(faces to the viewer, OpenGL RH) to the function. My tangent is OK but my bitangent is (0,-1,0). I think it should be (0,1,0). What's the problem? I hope you can help me! Here is the source code of my test program and the output of it:
#include <stdio.h>
#include <string.h>
#include "Vector4D.h"


struct Triangle
{
    unsigned short  index[3];
};


void CalculateTangentArray(long vertexCount, const Point3D *vertex, const Vector3D *normal,
        const Point2D *texcoord, long triangleCount, const Triangle *triangle, Vector4D *tangent)
{
    Vector3D *tan1 = new Vector3D[vertexCount * 2];
    Vector3D *tan2 = tan1 + vertexCount;
    // ClearMemory(tan1, vertexCount * sizeof(Vector3D) * 2);		Not available
	memset(tan1, NULL, vertexCount * sizeof(Vector3D) * 2);
    
    for (long a = 0; a < triangleCount; a++)
    {
        long i1 = triangle->index[0];
        long i2 = triangle->index[1];
        long i3 = triangle->index[2];
        
        const Point3D& v1 = vertex[i1];
        const Point3D& v2 = vertex[i2];
        const Point3D& v3 = vertex[i3];
        
        const Point2D& w1 = texcoord[i1];
        const Point2D& w2 = texcoord[i2];
        const Point2D& w3 = texcoord[i3];
        
        float x1 = v2.x - v1.x;
        float x2 = v3.x - v1.x;
        float y1 = v2.y - v1.y;
        float y2 = v3.y - v1.y;
        float z1 = v2.z - v1.z;
        float z2 = v3.z - v1.z;
        
        float s1 = w2.x - w1.x;
        float s2 = w3.x - w1.x;
        float t1 = w2.y - w1.y;
        float t2 = w3.y - w1.y;
        
        float r = 1.0F / (s1 * t2 - s2 * t1);
        Vector3D sdir((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r,
                (t2 * z1 - t1 * z2) * r);
        Vector3D tdir((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r,
                (s1 * z2 - s2 * z1) * r);
        
        tan1[i1] += sdir;
        tan1[i2] += sdir;
        tan1[i3] += sdir;
        
        tan2[i1] += tdir;
        tan2[i2] += tdir;
        tan2[i3] += tdir;
        
        triangle++;
    }
    
    for (long a = 0; a < vertexCount; a++)
    {
        const Vector3D& n = normal[a];
        const Vector3D& t = tan1[a];
        
        // Gram-Schmidt orthogonalize
        tangent[a] = (t - n * Dot(n, t)).Normalize();
        
        // Calculate handedness
        tangent[a].w = (Dot(Cross(n, t), tan2[a]) < 0.0F) ? -1.0F : 1.0F;
    }
    
    delete[] tan1;
}


int main()
{
	Point3D vertices[3];
	Point2D texcoords[3];
	Vector3D normals[3];
	Vector4D tangents[3];
	Vector3D bitangents[3];
	struct Triangle Tri = { 0, 1, 2 };
	int count = 0;


	vertices[0].x = -0.5;	vertices[0].y = -0.5;	vertices[0].z = -2.0;	// left, down
	vertices[1].x = 0.5;	vertices[1].y = -0.5;	vertices[1].z = -2.0;	// right, down
	vertices[2].x = -0.5;	vertices[2].y = 0.5;	vertices[2].z = -2.0;	// left, up

	texcoords[0].x = 0.0;	texcoords[0].y = 0.0;							// left, down
	texcoords[1].x = 1.0;	texcoords[1].y = 0.0;							// right, down
	texcoords[2].x = 0.0;	texcoords[2].y = 1.0;							// left, up

	normals[1].x = 0.0;		normals[0].y = 0.0;		normals[0].z = 1.0;		// faces to the viewer
	normals[2].x = 0.0;		normals[1].y = 0.0;		normals[1].z = 1.0;		// faces to the viewer
	normals[2].x = 0.0;		normals[2].y = 0.0;		normals[2].z = 1.0;		// faces to the viewer


	CalculateTangentArray(3, vertices, normals, texcoords, 1, &Tri, tangents);

	for (count = 0; count < 3; count++)
	{
		// BiTangent = cross(tangent, normal) * tangent.w;
		bitangents[count] = (tangents[count] % normals[count]) * tangents[count].w;
	}


	for (count = 0; count < 3; count++)
	{
		printf("\n\nTriangle Index: %d\n", count);
		printf("-----------------\n");
		printf("Vertex:               X: %f  Y: %f  Z %f\n", vertices[count].x, vertices[count].y, vertices[count].z);
		printf("Texture Coordinate:   U: %f  V: %f\n", texcoords[count].x, texcoords[count].y);
		printf("Normal:               X: %f  Y: %f  Z: %f\n", normals[count].x, normals[count].y, normals[count].z);
		printf("Tangent:              X: %f  Y: %f  Z: %f    W: %f\n", tangents[count].x, tangents[count].y, tangents[count].z, tangents[count].w);
		printf("BiTangent:            X: %f  Y: %f  Z: %f\n", bitangents[count].x, bitangents[count].y, bitangents[count].z);
	}

	return 0;
}

Here is the output: Triangle Index: 0 ----------------- Vertex: X: -0.500000 Y: -0.500000 Z -2.000000 Texture Coordinate: U: 0.000000 V: 0.000000 Normal: X: 0.000000 Y: 0.000000 Z: 1.000000 Tangent: X: 1.000000 Y: 0.000000 Z: -0.000000 W: 1.000000 BiTangent: X: 0.000000 Y: -1.000000 Z: 0.000000 Triangle Index: 1 ----------------- Vertex: X: 0.500000 Y: -0.500000 Z -2.000000 Texture Coordinate: U: 1.000000 V: 0.000000 Normal: X: 0.000000 Y: 0.000000 Z: 1.000000 Tangent: X: 1.000000 Y: 0.000000 Z: 0.000000 W: 1.000000 BiTangent: X: 0.000000 Y: -1.000000 Z: 0.000000 Triangle Index: 2 ----------------- Vertex: X: -0.500000 Y: 0.500000 Z -2.000000 Texture Coordinate: U: 0.000000 V: 1.000000 Normal: X: 0.000000 Y: 0.000000 Z: 1.000000 Tangent: X: 1.000000 Y: 0.000000 Z: 0.000000 W: 1.000000 BiTangent: X: 0.000000 Y: -1.000000 Z: 0.000000

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I calculate my Bitangents with that same code,

bitangents[a] = Cross(n, tangents[a]);
// Calculate handedness
bitangents[a] *=(Dot(Cross(n, t), tan2[a]) < 0.0F) ? -1.0F : 1.0F;

otherwise you need to do it in the VS and use the tangent.w component to flip the bitangent. IIRC

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This line is the problem:


bitangents[count] = (tangents[count] % normals[count]) * tangents[count].w;



Your cross product should be Cross(normal, tangent). By reversing the order of the operands, you've negated your bitangent.

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Thank you Eric, you make my day!

Two more questions regarding your "very welcome" code:

1.
Handedness of the vertex data doesn't matter. As long as you multiply the bitangent by the w component of the tangent you get correct vectors which uses the handedness of the input vertex data.
Is this correct?

2.
I believe I read somewhere that a perfect aligned cube (a origin aligned cube) can cause troubles with this code? I think it has to do with divison by zero?
Are there any problems?

Thank you very much, you helped me alot!

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Quote:
Original post by DOT31.
Handedness of the vertex data doesn't matter. As long as you multiply the bitangent by the w component of the tangent you get correct vectors which uses the handedness of the input vertex data.
Is this correct?


Yes, that's correct. Multiplying by the w component of the tangent after computing N x T takes care of orienting the bitangent to reflect the handedness at a vertex.

Quote:
Original post by DOT32.
I believe I read somewhere that a perfect aligned cube (a origin aligned cube) can cause troubles with this code? I think it has to do with divison by zero?
Are there any problems?


No, this is not a problem. The only way you can get a division by zero is if two vertices are in the exact same (x,y,z) position (which would be a bad mesh with degenerate triangles) or two vertices in a triangle have exactly the same (s,t) texture coordinates (which would be bad texture mapping).

Now there are other code snippets floating around out there that will react badly to perfectly aligned vertices or texture mapping (e.g., there are two vertices in a triangle that have exactly the same x coordinate, but differ in y and z), but those pieces of code are flawed. I amazed to see how much of that still exists even though I published the correct solution way back in 2001.

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      normalize all the vertices on my vertex shader i can get a perfect sphere.
      T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, 1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(180.0), glm::dvec3(1.0, 0.0, 0.0)); sides[0] = new TerrainNode(1.0, radius, T * R, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_FRONT)); T = glm::translate(glm::dmat4(1.0), glm::dvec3(0.0, 0.0, -1.0)); R = glm::rotate(glm::dmat4(1.0), glm::radians(0.0), glm::dvec3(1.0, 0.0, 0.0)); sides[1] = new TerrainNode(1.0, radius, R * T, glm::dvec2(0.0, 0.0), new TerrainTile(1.0, SIDE_BACK)); // So on and so forth for the rest of the sides As you can see, for the front side grid, i rotate it 180 degrees to make it face the camera and push it towards the eye;
      the back side is handled almost the same way only that i don't need to rotate it but simply push it away from the eye.
      The same technique is applied for the rest of the faces (obviously, with the proper rotations / translations).
      The matrix that result from the multiplication of R and T (in that particular order) is send to my vertex shader as `r_Grid'.
      // spherify vec3 V = normalize((r_Grid * vec4(r_Vertex, 1.0)).xyz); gl_Position = r_ModelViewProjection * vec4(V, 1.0); The `r_ModelViewProjection' matrix is generated on the CPU in this manner.
      // No the most efficient way, but it works. glm::dmat4 Camera::getMatrix() { // Create the view matrix // Roll, Yaw and Pitch are all quaternions. glm::dmat4 View = glm::toMat4(Roll) * glm::toMat4(Pitch) * glm::toMat4(Yaw); // The model matrix is generated by translating in the oposite direction of the camera. glm::dmat4 Model = glm::translate(glm::dmat4(1.0), -Position); // Projection = glm::perspective(fovY, aspect, zNear, zFar); // zNear = 0.1, zFar = 1.0995116e12 return Projection * View * Model; } I managed to get rid of z-fighting by using a technique called Logarithmic Depth Buffer described in this article; it works amazingly well, no z-fighting at all, at least not visible.
      Each frame i'm rendering each node by sending the generated matrices this way.
      // set the r_ModelViewProjection uniform // Sneak in the mRadiusMatrix which is a matrix that contains the radius of my planet. Shader::setUniform(0, Camera::getInstance()->getMatrix() * mRadiusMatrix); // set the r_Grid matrix uniform i created earlier. Shader::setUniform(1, r_Grid); grid->render(); My planet's radius is around 6400000.0 units, absurdly large, but that's what i really want to achieve;
      Everything works well, the node's split and merge as you'd expect, however whenever i get close to the surface
      of the planet the rounding errors start to kick in giving me that lovely stairs effect.
      I've read that if i could render each grid relative to the camera i could get better precision on the surface, effectively
      getting rid of those rounding errors.
       
      My question is how can i achieve this relative to camera rendering in my scenario here?
      I know that i have to do most of the work on the CPU with double, and that's exactly what i'm doing.
      I only use double on the CPU side where i also do most of the matrix multiplications.
      As you can see from my vertex shader i only do the usual r_ModelViewProjection * (some vertex coords).
       
      Thank you for your suggestions!
       
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