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Asked: 2025-06-14T04:14:30+05:30

How can I implement bicubic sampling for arbitrary data types in my raytracer’s texture interpolation?

I’m trying to add bicubic filtering to my software raytracer, but I’m kind of stuck on how to implement bicubic sampling for arbitrary data types in my texture interpolation. I already have a `Data` struct that has a bunch of operators defined to support arithmetic, but translating that into a bicubic interpolation is proving a bit tricky for me.

I found some references online that show how to do bicubic interpolation for `Vec4` types, which is great, but I need something that can handle any type of data. For example, my `Data` struct looks like this:

“`cpp
struct Data
{
Data operator+(const Data& val) const;
bool operator==(const Data& other);
bool operator!=(const Data& other);
Data& operator=(const Data& other);
Data operator*(const float& val) const;
//…
private:
float m_values[11];
};
“`

I already have bilinear interpolation implemented, and it works fine, but it just doesn’t give me the smoothness I’m after. I would like to implement the `BicubicSampling` method, but I’m overwhelmed by all the math and how to adapt it for a generic data type.

I know that bicubic interpolation generally uses a weighted average of 16 pixels (the 4×4 neighborhood) based on their distances to the target pixel. However, I’m not clear on how to calculate those weights and how to integrate the operations within my `Data` struct.

Here’s my existing bilinear function for reference:

“`cpp
template
inline T TImage::BilinearSampling(const Math::Vec2& texCoord) const {
// Existing bilinear code
}
“`

I’m thinking I might need something like four interpolation functions to handle the edge cases in the 4×4 grid for bicubic interpolation, but again, it’s hard to visualize how to make that work without knowing dimensions and weight calculations clearly.

I’ve gotten lost looking at various sources, including the Wikipedia page on bicubic interpolation, which only adds to the confusion. How can I effectively implement `BicubicSampling` for my `Data` struct? Any clear steps or code sketches to guide me in the right direction would be hugely appreciated!

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    2 Answers

    1. To implement bicubic interpolation for your generic Data struct, you can treat the problem similarly to your existing bilinear sampling, but perform the interpolation in two stages along each dimension. First, define a one-dimensional cubic interpolation function that takes four neighboring points along one axis and their corresponding fractional position (ranging from 0 to 1), performing weighted sums based on standard cubic interpolation coefficients. Your Data struct already has arithmetic operations (operator+, operator*) defined, which will enable you to combine these four data points easily with scalar weights in each interpolation step.

      With this 1D interpolation in hand, the bicubic interpolation simplifies to applying your cubic interpolation function first along rows to collapse the 4×4 neighborhood into four intermediate values, then along the column of these four intermediate results using the fractional coordinate in the other dimension. By decomposing bicubic interpolation into sequential 1D interpolations, your implementation will become straightforward and adaptable to any generic data type. Clearly separate the coefficient calculation logic (e.g. cubic spline or Catmull-Rom spline coefficients) from data interpolation, and you’ll obtain a clean, reusable solution capable of smoothly interpolating arbitrary data types like your Data struct.

    2. Bicubic Filtering Implementation for Custom Data Types

      Implementing bicubic sampling for your custom `Data` struct can be a bit challenging, but let’s break it down into manageable steps.

      Understanding Bicubic Interpolation

      Bicubic interpolation uses a weighted average of a 4×4 grid of pixels surrounding the target pixel. The weights are calculated based on the distances from the target pixel to each pixel in the grid. Here’s how you can start:

      Step 1: Create a Weight Calculation Function

      You need a function that computes the weights based on the relative distances. The general formula for bicubic weights is based on the cubic Hermite polynomials.

      
    float CubicWeight(float t) {
        if (t < 0) t = -t;
        if (t < 1) return (1.0f - 2.0f * t * t + t * t * t);
        if (t < 2) return (4.0f - 8.0f * t + 5.0f * t * t - t * t * t);
        return 0.0f;
    }

      Step 2: Implement the Bicubic Sampling Function

      Your function will take a texture coordinate and use it to find the relevant textures. You'll need to fetch 16 neighboring pixels (assuming you have some way to access them as `Data` types).

      
    template <typename T>
    T TImage<T>::BicubicSampling(const Math::Vec2& texCoord) const {
        // Get integer coordinates of the 4x4 grid
        int x = static_cast(texCoord.x);
        int y = static_cast(texCoord.y);
        
        // Calculate fractional offsets
        float xDiff = texCoord.x - x;
        float yDiff = texCoord.y - y;

        // Create an array for weights
        Data results[4][4];
        float weights[4][4];
        
        // Fetch the neighbors and calculate weights
        for (int i = -1; i <= 2; ++i) {
            for (int j = -1; j <= 2; ++j) {
                // Get neighbors here (be sure to handle texture edges)
                results[i + 1][j + 1] = GetTextureData(x + i, y + j); 
                weights[i + 1][j + 1] = CubicWeight(i - xDiff) * CubicWeight(j - yDiff);
            }
        }
        
        // Now perform the weighted average
        Data finalResult;
        float totalWeight = 0.0f;
        
        for (int i = 0; i < 4; ++i) {
            for (int j = 0; j < 4; ++j) {
                finalResult = finalResult + results[i][j] * weights[i][j];
                totalWeight += weights[i][j];
            }
        }
        
        // Normalize the result
        if (totalWeight > 0) {
            finalResult = finalResult * (1.0f / totalWeight);
        }
        
        return finalResult;
    }

      Step 3: Edge Case Handling

      Make sure your `GetTextureData` function properly handles edge cases, so you don't access out-of-bounds data in texture grids.

      Conclusion

      This is a basic outline of how to implement bicubic sampling for your `Data` struct. The key parts are calculating the weights and making sure to handle the additional complexity of arbitrary data types correctly. Test thoroughly and refine based on your needs!