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Texture coordinates at a point on triangle

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Hi, i seem to have trouble figuring out texture mapping coordinates on a random point that is on a 3D triangle. i know the texture coordinates on the corners and i know where the point is on triangle, but it seems complicated to find out what the texture coordinates are for the random point. i tried the barycentric coordinates but i couldn't get them to work cause i didn't understand that much. Can anybody point some directions? EDIT:SOLVED from given a triangle with corners p1,p2,p3 ,UVs: uv1,uv2,uv3 and a point on triangle called newp then the uv coordinates are:
    // Compute vectors 
    cml::vector3f v0 = p3 - p1;
    cml::vector3f v1 = p2 - p1;
    cml::vector3f v2 = newp - p1;

    // Compute dot products
    float dot00 = cml::dot(v0, v0);
    float dot01 = cml::dot(v0, v1);
    float dot02 = cml::dot(v0, v2);
    float dot11 = cml::dot(v1, v1);
    float dot12 = cml::dot(v1, v2);

    // Compute barycentric coordinates
    float invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
    float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
    float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
    cml::vector2f t2 = uv2-uv1;
    cml::vector2f t1 = uv3-uv1;

    cml::vector2f newuv = uv1 + t1*u + t2*v;

[Edited by - indexunknown on April 28, 2010 1:37:41 PM]

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Some C++ code aswell :


// 2 random numbers
float s = randgen.rand();
float t = randgen.rand();

// From Graphic Gems 1
float a = 1 - (float)sqrt(t);
float b = (1-s) * (float)sqrt(t);
float c = s * (float)sqrt(t);

// texcoord : pt0 texcoords of the edge0 of the triangle, etc..
vec2 sampletcoord = pt0*a + pt1*b + pt2*c;


Enjoy !

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thanks szecs, i tried your code from the second link where you make the triangle coordinate systems, but i seem to have big errors.

example output for 1 new point:
new point = (5.72205e-006, 20.4426, 46.072)
p1 = (5.19205, 20.4426, 46.072) , p2 = (-4.7633, 20.4426, 46.072) , p3 = (-4.76329, 11.026, 46.072)
uv1 = (1, 1) , uv2 = (0, 1) , uv3 = (0, 0)
e1 = (-9.95535, 1.90735e-006, 0) , e2 = (-9.95535, -9.41661, -3.8147e-006), n = (-1, 3.6736e-007, 0)
x_a = (-1, 1.9159e-007, 0) , y_a = (-1.9159e-007, -1, -4.05103e-007)
(x_a1,y_a1) = (9.95535, 2.27374e-013) , (x_a2,y_a2) = (9.95535, 9.41661)
m_a = (x_am,y_am) = (1, -1.75769e-007) , mb = (x_bm,y_bm) = (1, -1.75769e-007)
m_b_mod = (x_m_mod,y_m_mod) = (0.100449, -1.86659e-008)
t1 = ( -1 0), t2 = ( -1 -1)
newUV = ( -6.26493e-008 1)

left-original , on the right with new points on the side

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I don't understand this:
"left-original , on the right with new points on the side"

Is it a ray-tracer?
Or do you just insert a new vertex into a triangle?

Please clarify what you want to do.
A wire-frame image would be useful too.

Ant which/where is the new point? Sorry, those numbers are hard to follow for me.

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its a cube with a texture, on the left of image is a side of it having 2 triangles, on the right, it has been split up into an octree so the 2 triangles are divided into like 8 small ones so the new triangles need uvs for their corners. i know such splitting is bad but i just need to do it point is one corner of one new triangle, i don't know which of them this one is but the triangles are all correct.

mspaint auto generated some wires:

[Edited by - indexunknown on April 28, 2010 10:40:12 AM]

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for(unsigned int i = 0; i< tris.size();i++){
std::vector<cml::vector3f> tri =;
std::vector<cml::vector2f> uvs;
for(unsigned int j = 0; j<3 ;j++){

cml::vector3f newp = tri[j];
if(newp == p1){
}else if(newp == p2){
}else if(newp == p3){

cml::vector3f e1 = p2 - p1;
cml::vector3f e2 = p3 - p1;
cml::vector3f n = cml::normalize(newp - p1);

cml::vector3f x_a = cml::normalize(e1);
cml::vector3f y_a = cml::normalize(cml::cross(cml::cross(e1,e2),e1));

float x_a1 = cml::dot(e1,x_a);
float y_a1 = cml::dot(e1,y_a);
float x_a2 = cml::dot(e2,x_a);
float y_a2 = cml::dot(e2,y_a);

float x_am = cml::dot(n,x_a);
float y_am = cml::dot(n,y_a);
cml::vector2f m_a =cml::vector2f(x_am,y_am);

float x_bm = x_am - ( x_a2/y_a2 )*y_am;
float y_bm = y_am;
cml::vector2f m_b =cml::vector2f(x_bm,y_bm);

float x_m_mod=x_bm/x_a1;
float y_m_mod=y_bm/y_a2;
cml::vector2f m_b_mod =cml::vector2f(x_m_mod,y_m_mod);

cml::vector2f t1 = uv2 - uv1;
cml::vector2f t2 = uv3 - uv1;

cml::vector2f newuvs = uv1 + t1*x_bm + t2*y_bm;


this->nodeMesh.back().material = o.material;
this->nodeMesh.back().material.diffuseColor[0] = rand()%60 *0.01f;
this->nodeMesh.back().material.diffuseColor[1] = rand()%60 *0.01f;
this->nodeMesh.back().material.diffuseColor[2] = rand()%60 *0.01f;
this->nodeMesh.back().material.diffuseColor[3] = 1.0f;
this->nodeMesh.back().normal = o.normals[index];
this->nodeMesh.back().p1 = tri[0];
this->nodeMesh.back().uv1 = uvs[0];
this->nodeMesh.back().p2 = tri[1];
this->nodeMesh.back().uv2 = uvs[1];
this->nodeMesh.back().p3 = tri[2];
this->nodeMesh.back().uv3 = uvs[2];

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if n = newp - p1, then i got lots of small images of the texture on every triangle.
if i then did
newuvs[0] = 260*newuvs[0]; texture size
newuvs[1] = 256*newuvs[1];
then i got a grey square and if after this i did
newuvs = cml::normalize(newuvs);
then its just random stretched mess.

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always post pictures please.

You don't have to multiply the result with the image sizes. Think a bit. Your original UVs are in 0...1.

This way you will get 0...2xx. Of course it's screwed.

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1)left picture: n = newp - p1;

2) middle picture:
n = newp - p1;
newuvs[0] = 260*newuvs[0]; texture size
newuvs[1] = 256*newuvs[1];
3) right picture:
n = newp - p1;
newuvs[0] = 260*newuvs[0]; texture size
newuvs[1] = 256*newuvs[1];
newuvs = cml::normalize(newuvs);

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