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C++ code to compute the inverse of a linearly-interpolated 1D table with values in [0, 1] x [0, 1] (note: the table size must be a power of two)
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| #include <cstdio> | |
| #include <cstdlib> | |
| #include <cmath> | |
| #include <vector> | |
| // inverting piecewise linear functions | |
| float InverseLinear(float yStart, float yEnd, float y) | |
| { | |
| return (y - yStart) / (yEnd - yStart); | |
| } | |
| float InverseLinearInterval(float xStart, float xEnd, | |
| float yStart, float yEnd, | |
| float y) | |
| { | |
| float scale = xEnd - xStart; | |
| float offset = xStart; | |
| return InverseLinear(yStart, yEnd, y) * scale + offset; | |
| } | |
| // inverts a function defined with values in [0, 1]x[0, 1] | |
| std::vector<float> Inverse(const std::vector<float>& cdf, int sizeLog2) | |
| { | |
| int size = (1 << sizeLog2); | |
| std::vector<float> qf(size, 0); | |
| for (int i = 0; i < size; ++i) { | |
| float u = (float)i / (size - 1); // in [0, 1] | |
| int index = size / 2; | |
| // binary search the value | |
| for (int j = sizeLog2 - 2; j >= 0; --j) { | |
| int offset = 1 << j; | |
| if (u <= cdf[index]) { | |
| index-= offset; | |
| } else { | |
| index+= offset; | |
| } | |
| } | |
| // invert linear segment | |
| if (u <= cdf[index]) { | |
| float xStart = (float)(index - 1) / (size - 1); | |
| float xEnd = (float)(index ) / (size - 1); | |
| qf[i] = InverseLinearInterval(xStart, xEnd, cdf[index - 1], cdf[index], u); | |
| } else { | |
| float xStart = (float)(index + 1) / (size - 1); | |
| float xEnd = (float)(index ) / (size - 1); | |
| qf[i] = InverseLinearInterval(xStart, xEnd, cdf[index + 1], cdf[index], u); | |
| } | |
| } | |
| return qf; | |
| } | |
| #if 0 // for experimenting | |
| // dumps a plot file for GNUPLOT | |
| // e.g., > plot './linear' u 1:2 w lines, '' u 1:3 w lines, '' u 1:4 w lines | |
| void print(const char *filename, const std::vector<float>& cdf, int sizeLog2) | |
| { | |
| FILE *pf = fopen(filename, "w"); | |
| int size = 1 << sizeLog2; | |
| std::vector<float> qf = Inverse(cdf, sizeLog2); | |
| for (int i = 0; i < size; ++i) { | |
| float u = (float)i / (size - 1); | |
| fprintf(pf, "%f %f %f %f \n", u, cdf[i], qf[i], u); | |
| } | |
| fclose(pf); | |
| } | |
| int main(int argc, char **argv) | |
| { | |
| int sizeLog2 = 8; | |
| int size = 1 << sizeLog2; | |
| std::vector<float> cdf(size); | |
| // linear | |
| for (int i = 0; i < size; ++i) { | |
| float u = (float)i / (size - 1); | |
| cdf[i] = u; | |
| } | |
| print("linear", cdf, sizeLog2); | |
| // square | |
| for (int i = 0; i < size; ++i) { | |
| float u = (float)i / (size - 1); | |
| cdf[i] = u * u; | |
| } | |
| print("square", cdf, sizeLog2); | |
| // quintic | |
| for (int i = 0; i < size; ++i) { | |
| float u = (float)i / (size - 1); | |
| cdf[i] = u * u * u * u * u; | |
| } | |
| print("quintic", cdf, sizeLog2); | |
| // sqrt | |
| for (int i = 0; i < size; ++i) { | |
| float u = (float)i / (size - 1); | |
| cdf[i] = sqrtf(u); | |
| } | |
| print("sqrt", cdf, sizeLog2); | |
| } | |
| #endif |
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