opengl,math,glsl , 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:

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:

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?

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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