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Merge pull request #2748 from Socolin/quad-distortion
Add QuadDistortion to ProjectiveTransformBuilder
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86 changes: 86 additions & 0 deletions
86
src/ImageSharp/Processing/Processors/Transforms/Linear/GaussianEliminationSolver.cs
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| // Copyright (c) Six Labors. | ||
| // Licensed under the Six Labors Split License. | ||
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| namespace SixLabors.ImageSharp.Processing.Processors.Transforms.Linear; | ||
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| /// <summary> | ||
| /// Represents a solver for systems of linear equations using the Gaussian Elimination method. | ||
| /// This class applies Gaussian Elimination to transform the matrix into row echelon form and then performs back substitution to find the solution vector. | ||
| /// This implementation is based on: <see href="https://www.algorithm-archive.org/contents/gaussian_elimination/gaussian_elimination.html"/> | ||
| /// </summary> | ||
| internal static class GaussianEliminationSolver | ||
| { | ||
| /// <summary> | ||
| /// Solves the system of linear equations represented by the given matrix and result vector using Gaussian Elimination. | ||
| /// </summary> | ||
| /// <param name="matrix">The square matrix representing the coefficients of the linear equations.</param> | ||
| /// <param name="result">The vector representing the constants on the right-hand side of the linear equations.</param> | ||
| /// <exception cref="Exception">Thrown if the matrix is singular and cannot be solved.</exception> | ||
| /// <remarks> | ||
| /// The matrix passed to this method must be a square matrix. | ||
| /// If the matrix is singular (i.e., has no unique solution), an <see cref="NotSupportedException"/> will be thrown. | ||
| /// </remarks> | ||
| public static void Solve(double[][] matrix, double[] result) | ||
| { | ||
| TransformToRowEchelonForm(matrix, result); | ||
| ApplyBackSubstitution(matrix, result); | ||
| } | ||
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| private static void TransformToRowEchelonForm(double[][] matrix, double[] result) | ||
| { | ||
| int colCount = matrix.Length; | ||
| int rowCount = matrix[0].Length; | ||
| int pivotRow = 0; | ||
| for (int pivotCol = 0; pivotCol < colCount; pivotCol++) | ||
| { | ||
| double maxValue = double.Abs(matrix[pivotRow][pivotCol]); | ||
| int maxIndex = pivotRow; | ||
| for (int r = pivotRow + 1; r < rowCount; r++) | ||
| { | ||
| double value = double.Abs(matrix[r][pivotCol]); | ||
| if (value > maxValue) | ||
| { | ||
| maxIndex = r; | ||
| maxValue = value; | ||
| } | ||
| } | ||
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| if (matrix[maxIndex][pivotCol] == 0) | ||
| { | ||
| throw new NotSupportedException("Matrix is singular and cannot be solve"); | ||
| } | ||
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| (matrix[pivotRow], matrix[maxIndex]) = (matrix[maxIndex], matrix[pivotRow]); | ||
| (result[pivotRow], result[maxIndex]) = (result[maxIndex], result[pivotRow]); | ||
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| for (int r = pivotRow + 1; r < rowCount; r++) | ||
| { | ||
| double fraction = matrix[r][pivotCol] / matrix[pivotRow][pivotCol]; | ||
| for (int c = pivotCol + 1; c < colCount; c++) | ||
| { | ||
| matrix[r][c] -= matrix[pivotRow][c] * fraction; | ||
| } | ||
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| result[r] -= result[pivotRow] * fraction; | ||
| matrix[r][pivotCol] = 0; | ||
| } | ||
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| pivotRow++; | ||
| } | ||
| } | ||
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| private static void ApplyBackSubstitution(double[][] matrix, double[] result) | ||
| { | ||
| int rowCount = matrix[0].Length; | ||
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| for (int row = rowCount - 1; row >= 0; row--) | ||
| { | ||
| result[row] /= matrix[row][row]; | ||
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| for (int r = 0; r < row; r++) | ||
| { | ||
| result[r] -= result[row] * matrix[r][row]; | ||
| } | ||
| } | ||
| } | ||
| } |
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