An HLSL function for sampling a 2D texture with Catmull-Rom filtering, using 9 texture samples instead of 16

Tex2DCatmullRom.hlsl

// The following code is licensed under the MIT license: https://gist.github.com/TheRealMJP/bc503b0b87b643d3505d41eab8b332ae

// Samples a texture with Catmull-Rom filtering, using 9 texture fetches instead of 16.
// See http://vec3.ca/bicubic-filtering-in-fewer-taps/ for more details
float4 SampleTextureCatmullRom(in Texture2D<float4> tex, in SamplerState linearSampler, in float2 uv, in float2 texSize)
{
    // We're going to sample a a 4x4 grid of texels surrounding the target UV coordinate. We'll do this by rounding
    // down the sample location to get the exact center of our "starting" texel. The starting texel will be at
    // location [1, 1] in the grid, where [0, 0] is the top left corner.
    float2 samplePos = uv * texSize;
    float2 texPos1 = floor(samplePos - 0.5f) + 0.5f;

    // Compute the fractional offset from our starting texel to our original sample location, which we'll
    // feed into the Catmull-Rom spline function to get our filter weights.
    float2 f = samplePos - texPos1;

    // Compute the Catmull-Rom weights using the fractional offset that we calculated earlier.
    // These equations are pre-expanded based on our knowledge of where the texels will be located,
    // which lets us avoid having to evaluate a piece-wise function.
    float2 w0 = f * (-0.5f + f * (1.0f - 0.5f * f));
    float2 w1 = 1.0f + f * f * (-2.5f + 1.5f * f);
    float2 w2 = f * (0.5f + f * (2.0f - 1.5f * f));
    float2 w3 = f * f * (-0.5f + 0.5f * f);

    // Work out weighting factors and sampling offsets that will let us use bilinear filtering to
    // simultaneously evaluate the middle 2 samples from the 4x4 grid.
    float2 w12 = w1 + w2;
    float2 offset12 = w2 / (w1 + w2);

    // Compute the final UV coordinates we'll use for sampling the texture
    float2 texPos0 = texPos1 - 1;
    float2 texPos3 = texPos1 + 2;
    float2 texPos12 = texPos1 + offset12;

    texPos0 /= texSize;
    texPos3 /= texSize;
    texPos12 /= texSize;

    float4 result = 0.0f;
    result += tex.SampleLevel(linearSampler, float2(texPos0.x, texPos0.y), 0.0f) * w0.x * w0.y;
    result += tex.SampleLevel(linearSampler, float2(texPos12.x, texPos0.y), 0.0f) * w12.x * w0.y;
    result += tex.SampleLevel(linearSampler, float2(texPos3.x, texPos0.y), 0.0f) * w3.x * w0.y;

    result += tex.SampleLevel(linearSampler, float2(texPos0.x, texPos12.y), 0.0f) * w0.x * w12.y;
    result += tex.SampleLevel(linearSampler, float2(texPos12.x, texPos12.y), 0.0f) * w12.x * w12.y;
    result += tex.SampleLevel(linearSampler, float2(texPos3.x, texPos12.y), 0.0f) * w3.x * w12.y;

    result += tex.SampleLevel(linearSampler, float2(texPos0.x, texPos3.y), 0.0f) * w0.x * w3.y;
    result += tex.SampleLevel(linearSampler, float2(texPos12.x, texPos3.y), 0.0f) * w12.x * w3.y;
    result += tex.SampleLevel(linearSampler, float2(texPos3.x, texPos3.y), 0.0f) * w3.x * w3.y;

    return result;
}

If you are doing the filtering yourself and you want to use a linear buffer, you can use rawBuffer0.Load4()
coherency might or might not be worse, it depends. Dynamic updates are usually easier.

For the 5 taps should we renormalize weights?
float weight = w12.x * w0.y + w0.x * w12.y + w12.x * w12.y + w3.x * w12.y + w12.x * w3.y;
result /= weight;