How do I make a set of blocks look seamless when I know the size of the texture and the position and dimensions of the blocks?

Question

So I have a seamless texture. The black lines in the picture represent the repeating texture. Then I have a series of blocks who have known x,y coordinates and known height and width. In Unity Textures have a 'scale' and 'offset'.

Scale is the amount of the texture that will show on the block. So the block starting at 0,0 will have a scale of about (.2,1.3). It's width is .2x the width of a single texture (for the sake of simple numbers) and it's height is about 1.3x the height of the texture.

Offset then moves the 'starting point of the texture. The block at 0,0 will have an offset of 0,0 because it is perfectly aligned with a corner but the block immediately to it's right would have a texture of about .2,0 because the texture needs to start about .2 units in to align properly. This is as far as I understand offset. I am pretty sure this is correct but feel free to correct me if I am wrong.

Now when you apply a texture to a block unity automatically scales the texture to start at the top left corner of the block and stretch it appropriately to fit 1 full iteration inside of that space. I obviously don't want this.

My question comes in for the three blocks labeled with the (x,y) coordinates. I have tried for several hours over a few weeks to get it right, unsuccessfully.

So how do I take in the x,y position and width/height to create a correct scale and offset so that those blocks will look like they are exactly where they are supposed to be in the texture?

It is not a particularly difficult concept but after staring at it I have no more ideas.

For the sake of the question assume a single texture is 12x12. The x,y and width/height are known values but are arbitrary.

I know it's normally good practice to post attempted code but I would rather see a good way of doing it than see answers that try to fix my failed attempts. But I will post code if people want to see that I did try on my own or how I initially tried.

Answer 1

What is a UV Map

Textures are applied to models by what is known as UV map. The idea is that each (x,y,z) vertex has two (u,v) coordinates assigned. UV coordinates define which point on the texture should correspond to that vertex. If you want to know more, I suggest the awesome (and free) Udacity 3D graphics course. Unit 8 talks about UV mapping.

How to solve your problem using UV Maps

Let's ignore all the vertices that are not visible - your blocks are basically rectangles. You can assign a UV mapping, where world possition of each vertex will be turned into its UV coordinate. This way, all the blocks will have the same origin point in texture space (0,0 in world position corresponds to 0,0 on texture). Code looks like this:

Mesh mesh = GetComponent<MeshFilter>().mesh;
Vector3[] vertices = mesh.vertices;
Vector2[] uvs = new Vector2[vertices.Length];

for (int i = 0; i < uvs.Length; i++)
{
    // Find world position of each point
    Vector3 vertexPos = transform.TransformPoint(vertices[i]);
    // And assign its x,y coordinates to u,v.
    uvs[i] = new Vector2(vertexPos.x, vertexPos.y);
}
mesh.uv = uvs;

You have to do this each time your block position changes.