How can I find the right UV coordinates for interpolating a bezier curve?

Question

I'll let this picture do the talking. I'm trying to create a mesh from a bezier curve and then add a texture to it. The problem here is that the interpolation points along the curve do not increase linearly, so points farther from the control point (near the endpoints) stretch and those in the bend contract, causing the texture to be uneven across the curve, which can be problematic when using a pattern like stripes on a road. How can I determine how far along the curve the vertices actually are so I can give a proper UV coordinate?

EDIT: Allow me to clarify that I'm not talking about the trapezoidal distortion of the roads. That I know is normal and I'm not concerned about. I've updated the image to show more clearly where my concerns are.

Interpolating over the curve I get 10 segments, but each of these 10 segments is not spaced at an equal point along the curve, so I have to account for this in assigning UV data to vertices or else the road texture will stretch/shrink depending on how far apart vertices are at that particular part of the curve.

Answer 1

A line is a list of connected points. For each point you'll need to calculate the X-Texture coordinate of that point, the Y coordinate will always be 0 for the upper point and 1 for the lower point.

After you have defined how long one texture segment is you can do so by stepping through all the segments you have generated and noting how much distance you have covered:

float pos = 0;
float textureLength = 200;
Points[0].TexCoord = 0;
for(int i = 1; i < Points.size(); ++i)
{
    pos += DistanceBetween(Points[i].Position, Points[i-1].Position);
    Points[i].TexCoord = pos / textureLength;
}

Answer 2

I'd suggest calculating UV according to section size (i guess U value would be constant), you know the size of the section, now calculate how many times road's texture should repeat along each edge (different V for each side according to size) and when you start drawing next section just set minimum values of V coordinate to the result of calculations of previous section.

Vector2 SetupSection(Vertex[6] aVertexes, Vector2 vPrevVValues)
{
    //lets consider that polygons are 0,1,2 and 3,4,5
    //where vertexes 0, 4 and 5 are bottom vertexes and 1, 2 and 3 are top vertexes (or min/max)
    //now lets calculate distance
    float fLeftDistance = (aVertexes[0].Position - aVertexes[1].position).Length();
    float vValue = fLeftDistance / fSizeModifier; //some constant decided by you
    aVertexes[0].v = aVertexes[4].v = vPrevValues.x; //Set left bottom to previous values
    aVertexes[5].v = vPrevValues.y; //set right bot to previous values
    vPrevValues.x += fLeftDistance;
    aVertexes[1].v = vPrevValues.x;

    float fRightDistance = (aVertexes[5].Position - aVertexes[3].position).Length();
    float vValue = fLeftDistance / fSizeModifier;
    vPrevValues.y += vValue;
    aVertexes[2].v = aVertexes[3].v = vPrevValues.y;
    return vPrevValue;//return new V values
}