opengl,math,glsl , Scaling part of mesh in a given direction


Scaling part of mesh in a given direction

Question:

Tag: opengl,math,glsl

I have a lot of cubes (ex 100) that are all part of the same mesh, and in a vertex shader I would like to scale each cube along a given axis, so it's top is moved and the cube stretched like this:

enter image description here enter image description here

Each cube has an ID, and each vertex has a corresponding ID, so each vertex knows what cube it is part of. A uniform array of vec3 normalized cubeUps (the direction the cubes should be expanding) and a uniform array of vec3 cubeOrigins (the base of each cube) is also passed to the shader. The indices of these uniform arrays match the ID's of the cubes.

Right know the cubeOrigins of the cubes are placed at the center of the bottom of each cube like the white dot here, because I think that is what's needed, but not sure:

enter image description here

I can very easily translate the cubes along the given normal like this:

layout (location = 0) in vec3 vertexPos;
layout (location = 1) in vec3 vertexNor;
layout (location = 2) in float vertexCubeId;

uniform mat4 mvp;

uniform vec3 cubeUps[100];
uniform vec3 cubeOrigins[100];

void main()
{
    int cubeIndex = int(vertexCubeId);
    vec3 cubeUp = cubeUps[cubeIndex];
    vec3 cubeOrigin = cubeOrigins[cubeIndex];

    vec3 transformedPos = vertexPos;

    transformedPos.x += cubeUp.x;
    transformedPos.y += cubeUp.y;
    transformedPos.z += cubeUp.z;

    gl_Position = mvp * vec4(transformedPos, 1.0);
}

but my plan for doing the scaling is not working out. What I think I need to do is:

  1. Subtract the origin from the vertex, to use a common base for the scaling.
  2. Do the scaling along the 'cubeUp' vector somehow.
  3. Add the origin to the vertex to move away from the base again.

Something like this:

...

float scaleFactor = 1.5f;
vec3 scale = cubeUp * scaleFactor;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

transformedPos.x *= scale.x;
transformedPos.y *= scale.y;
transformedPos.z *= scale.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

gl_Position = mvp * vec4(transformedPos, 1.0);

...

But this both moves the cubes to undesired positions, and doesn't scale them correctly.

Do I somehow need to rotate the vertex coordinates before applying the scale, in order to use the origin correctly?

How do I get from the given cubeUp vector to the correct values to use for the scaling?


Answer:

Take the dot product of the vertex (after subtracting the origin) in the direction of cubeUp and then scale it and add to the vertex position. This will ensure that the vertices only move in the direction of cubeUp. Something like this:

float scaleFactor = 1.5f;

transformedPos.x -= cubeOrigin.x;
transformedPos.y -= cubeOrigin.y;
transformedPos.z -= cubeOrigin.z;

float dotProduct = dot(cubeUp, transformedPos);
dotProduct *= (scaleFactor - 1.0f);   // or just set scaleFactor
                                      // to 0.5f in the first place
vec3 offset = cubeUp * dotProduct;

transformedPos.x += offset.x;
transformedPos.y += offset.y;
transformedPos.z += offset.z;

transformedPos.x += cubeOrigin.x;
transformedPos.y += cubeOrigin.y;
transformedPos.z += cubeOrigin.z;

To visualize why simply multiplying by a scale vector doesn't work, imagine a vertex on the plane defined by cubeOrigin and cubeUp (i.e. the base of the cube). It shouldn't move at all. However each of the corner vertices is going to have a non-zero transformedPos vector, which means that the values will not be the same after multiplying by scale, except in the special case where cubeUp points exactly along the X Y or Z axis.

You need to specifically multiply just that part of the transformedPos vector that is in the direction of cubeUp, which is equal to dot(cubeUp, transformedPos) * cubeUp. Instead of subtracting that part then multiplying by 1.5 then re-adding it, it's more efficient to just multiply by 0.5 and add it.


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