Curious Transparent Holes Render Artifact

Question

So I'm trying to implement "smooth" terrain in my block engine by giving each surface block a heightmap.

Basically, what I do to generate these "heightmaps" for each block is I generate the heights at intervals of 0.25 along the edge of the block. Then, to build the block's vertices, I loop through the heights and create triangles from height to height and put rectangles under the triangles to create something like this:

For example, to build the X positive side of a block, I do:

                    Vector2[] uv = BlockUtil.UVMappings[(byte)side]; // uv[0] = top left

                    float height;
                    float nextHeight;
                    float min;

                    float tex_len = 1f / EngineGlobals.TEXTURE_ATLAS_SIDE;

                    for (int i = 0; i < 4; i++)
                    {
                        height = (float)b.Heights[4, i] / 255f;

                        nextHeight = (float)b.Heights[4, i + 1] / 255f;

                        min = Math.Min(height, nextHeight);

                        //create the triangles at the top
                        if (nextHeight > height)
                        {
                            int offset = ch.vertexMap.Count;

                            AddVertex(ch, 0, 0, uv[0] + new Vector2(tex_len * (i / 4f), (1-height)*tex_len), blockPos, new Vector3(1f, height, i / 4f), tr, isliquid);
                            AddVertex(ch, 0, 0, uv[0] + new Vector2(tex_len * ((i + 1) / 4f), 0), blockPos, new Vector3(1f, height, (i + 1) / 4f), tr, isliquid);
                            AddVertex(ch, 0, 0, uv[0] + new Vector2(tex_len * ((i + 1) / 4f), 0), blockPos, new Vector3(1f, nextHeight, (i + 1) / 4f), tr, isliquid);

                            AddTriIndices(offset, 0, 1, 2);
                        }
                        else if (nextHeight < height)
                        {
                            int offset = ch.vertexMap.Count;

                            AddVertex(ch, 0, 0, uv[0] + new Vector2(tex_len * (i / 4f), (1-height)*tex_len), blockPos, new Vector3(1f, height, i / 4f), tr, isliquid);
                            AddVertex(ch, 0, 0, uv[0] + new Vector2(tex_len * (i / 4f), (1-nextHeight)*tex_len), blockPos, new Vector3(1f, nextHeight, i / 4f), tr, isliquid);
                            AddVertex(ch, 0, 0, uv[0] + new Vector2(tex_len * ((i + 1) / 4f), (1 - nextHeight) * tex_len), blockPos, new Vector3(1f, nextHeight, (i + 1) / 4f), tr, isliquid);

                            AddTriIndices(offset, 0, 1, 2);
                        }
                        // else: heights are equal; ignore

                        // create the base rectangle
                        AddVertex(ch, 0, 0, uv[0] + new Vector2(tex_len * (float)i / 4f + tex_len / 4f, (1 - min) * tex_len), blockPos, new Vector3(1, min, (float)(i + 1) / 4f), tr, isliquid);
                        AddVertex(ch, 0, 1, uv[0] + new Vector2(tex_len * (float)i/4f, (1 - min) * tex_len), blockPos, new Vector3(1, min, (float)i / 4f), tr, isliquid);
                        AddVertex(ch, 0, 2, uv[0] + new Vector2(tex_len * (float)i / 4f + tex_len / 4f, tex_len), blockPos, new Vector3(1, 0, (float)(i + 1) / 4f), tr, isliquid);
                        AddVertex(ch, 0, 3, uv[0] + new Vector2(tex_len * (float)i / 4f, tex_len), blockPos, new Vector3(1, 0, (float)i / 4f), tr, isliquid);

                        AddIndices(ch, 0, 1, 2, 2, 1, 3, isliquid);
                    }

I'm not sure if this is a floating point precision error, but when I render it, I get these curious holes on the borders of the base rectangles (I know they're holes because their colors match the color behind them)

What really throws me off is that rather than a whole line, it's just seemingly random dots.

A wireframe view of the world did not reveal any discrepancies. (all it did was make the game lag)

A quick little hack that I did was to extend the (i+1)/4 in the code to (i+1.01f)/4, but I'd rather get a concrete solution than something like that.

Perhaps it's something in my shader? My texture sampler is:

Texture TextureAtlas;
sampler TextureSampler = sampler_state
{
        texture = <TextureAtlas>;
    magfilter = POINT;
    minfilter = POINT;
    mipfilter = POINT;
    AddressU = WRAP;
    AddressV = WRAP;
};

Thanks in advance!

Answer 1

From your diagram, it looks like the geometry you're constructing contains T-junctions - places where a vertex of one triangle is supposed to lie exactly on another triangle's edge (resulting in one edge meeting another in a "T" shape). Due to the limitations of finite-precision arithmetic, the vertex usually cannot be guaranteed to meet the edge perfectly and you will find microscopic cracks between them, which often show up as single-pixel glitches because an individual pixel may happen to land in the crack while its neighbors don't.

To fix it, you have to build your geometry in such a way that there are no T-junctions, by splitting each edge where a vertex is supposed to meet it. This diagram shows an example:

EDIT: The above applies to T-junctions in general. For your specific case, as Ilmari Karonen pointed out in the comments, you can build the geometry even better like this:

which also avoids T-junctions and has fewer triangles overall.