Tag: Algorithms

I have a network that is straight and I change it to follow along a Bezier curve. The problem is that mesh textures are stretched / contracted depending on the shape of the curve. Since Bezier curves do not have a constant slope, I had to use a lookup table for every net I want to bend.

The lookup table distributes the vertices and UVs evenly along the curve so that the textures look correct. But I was wondering if there was any way to do this without using a lookup table, because I would like to use a shader and would prefer not having to create arrays of spaces in my shader for each curve myself.

Is that even possible? I could not imagine an algorithm for it, so I wondered if anyone knew of a way to do it without a look-up table.

This is my current LUT approach in C #:

    private static void SetDistances(CubicBezier cb)
    {
        _LUT(0) = 0;
        Vector3 prevPoint = cb.A;
        float precisionm1 = Precision - 1;

        for (int i = 1; i < _LUT.Length; i++)
        {
            float t = i / precisionm1;
            var pos = cb.Evaluate(t);
            var delta = (prevPoint - pos).magnitude;
            _LUT(i) = _LUT(i - 1) + delta;
            prevPoint = pos;
        }
    }

    public static float Percentage(float t, CubicBezier cb)
    {
        SetDistances(cb);

        float iFloat = t * (Precision - 1);
        int idLower = (int)iFloat;
        int idUpper = idLower + 1;

        if (idUpper >= _LUT.Length)
        {
            idUpper = _LUT.Length - 1;
        }
        if (idLower < 0)
        {
            idLower = 0;
        }

        float result = Mathf.Lerp(_LUT(idLower), _LUT(idUpper), iFloat - idLower) / cb.Length;
        return result;
    }

Code that changes the network:

    for (int i = 0; i < _vertices.Length; i++)
    {
        Vector3 v = _vertices(i);
        float t = v.z / _subDivisions;
        Vector3 pos = _cb.Evaluate(t);
        Vector3 perp = _cb.Perp(t);
        if (Mathf.Abs(v.x) <= Mathf.Epsilon)
        {
            _newVerts(i) = pos;
        }
        else
        {
            _newVerts(i) = pos + perp * v.x;
        }
        _newVerts(i).y = v.y + pos.y;
        _newuvs(i) = new Vector2(_uvs(i).x, Bezier.Percentage(t,_cb) * _cb.Length);
    }