@ -3,6 +3,7 @@
using System.Numerics ; using System.Numerics ;
using System.Runtime.CompilerServices ; using System.Runtime.CompilerServices ;
using SixLabors.ImageSharp.Processing.Processors.Transforms.Linear ;
namespace SixLabors.ImageSharp.Processing.Processors.Transforms ; namespace SixLabors.ImageSharp.Processing.Processors.Transforms ;
@ -278,6 +279,91 @@ internal static class TransformUtils
return matrix ; return matrix ;
} }
/// <summary>
/// Computes the projection matrix for a quad distortion transformation.
/// </summary>
/// <param name="rectangle">The source rectangle.</param>
/// <param name="topLeft">The top-left point of the distorted quad.</param>
/// <param name="topRight">The top-right point of the distorted quad.</param>
/// <param name="bottomRight">The bottom-right point of the distorted quad.</param>
/// <param name="bottomLeft">The bottom-left point of the distorted quad.</param>
/// <param name="transformSpace">The <see cref="TransformSpace"/> to use when creating the matrix.</param>
/// <returns>The computed projection matrix for the quad distortion.</returns>
/// <remarks>
/// This method is based on the algorithm described in the following article:
/// <see href="https://blog.mbedded.ninja/mathematics/geometry/projective-transformations/"/>
/// </remarks>
public static Matrix4x4 CreateQuadDistortionMatrix (
Rectangle rectangle ,
PointF topLeft ,
PointF topRight ,
PointF bottomRight ,
PointF bottomLeft ,
TransformSpace transformSpace )
{
PointF p1 = new ( rectangle . X , rectangle . Y ) ;
PointF p2 = new ( rectangle . X + rectangle . Width , rectangle . Y ) ;
PointF p3 = new ( rectangle . X + rectangle . Width , rectangle . Y + rectangle . Height ) ;
PointF p4 = new ( rectangle . X , rectangle . Y + rectangle . Height ) ;
PointF q1 = topLeft ;
PointF q2 = topRight ;
PointF q3 = bottomRight ;
PointF q4 = bottomLeft ;
double [ ] [ ] matrixData =
[
[p1.X, p1.Y, 1, 0, 0, 0, -p1.X * q1.X, -p1.Y * q1.X] ,
[0, 0, 0, p1.X, p1.Y, 1, -p1.X * q1.Y, -p1.Y * q1.Y] ,
[p2.X, p2.Y, 1, 0, 0, 0, -p2.X * q2.X, -p2.Y * q2.X] ,
[0, 0, 0, p2.X, p2.Y, 1, -p2.X * q2.Y, -p2.Y * q2.Y] ,
[p3.X, p3.Y, 1, 0, 0, 0, -p3.X * q3.X, -p3.Y * q3.X] ,
[0, 0, 0, p3.X, p3.Y, 1, -p3.X * q3.Y, -p3.Y * q3.Y] ,
[p4.X, p4.Y, 1, 0, 0, 0, -p4.X * q4.X, -p4.Y * q4.X] ,
[0, 0, 0, p4.X, p4.Y, 1, -p4.X * q4.Y, -p4.Y * q4.Y] ,
] ;
double [ ] b =
[
q1 . X ,
q1 . Y ,
q2 . X ,
q2 . Y ,
q3 . X ,
q3 . Y ,
q4 . X ,
q4 . Y ,
] ;
GaussianEliminationSolver . Solve ( matrixData , b ) ;
#pragma warning disable SA1117
Matrix4x4 projectionMatrix = new (
( float ) b [ 0 ] , ( float ) b [ 3 ] , 0 , ( float ) b [ 6 ] ,
( float ) b [ 1 ] , ( float ) b [ 4 ] , 0 , ( float ) b [ 7 ] ,
0 , 0 , 1 , 0 ,
( float ) b [ 2 ] , ( float ) b [ 5 ] , 0 , 1 ) ;
#pragma warning restore SA1117
// Check if the matrix involves only affine transformations by inspecting the relevant components.
// We want to use pixel space for calculations only if the transformation is purely 2D and does not include
// any perspective effects, non-standard scaling, or unusual translations that could distort the image.
if ( transformSpace = = TransformSpace . Pixel & & IsAffineRotationOrSkew ( projectionMatrix ) )
{
if ( projectionMatrix . M41 ! = 0 )
{
projectionMatrix . M41 - - ;
}
if ( projectionMatrix . M42 ! = 0 )
{
projectionMatrix . M42 - - ;
}
}
return projectionMatrix ;
}
/// <summary>
/// <summary>
/// Returns the size relative to the source for the given transformation matrix.
/// Returns the size relative to the source for the given transformation matrix.
/// </summary>
/// </summary>
@ -293,15 +379,16 @@ internal static class TransformUtils
/// </summary>
/// </summary>
/// <param name="matrix">The transformation matrix.</param>
/// <param name="matrix">The transformation matrix.</param>
/// <param name="size">The source size.</param>
/// <param name="size">The source size.</param>
/// <param name="transformSpace">The <see cref="TransformSpace"/> used when generating the matrix.</param>
/// <returns>
/// <returns>
/// The <see cref="Size"/>.
/// The <see cref="Size"/>.
/// </returns>
/// </returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Size GetTransformedSize ( Matrix4x4 matrix , Size size ) public static Size GetTransformedSize ( Matrix4x4 matrix , Size size , TransformSpace transformSpace )
{ {
Guard . IsTrue ( size . Width > 0 & & size . Height > 0 , nameof ( size ) , "Source size dimensions cannot be 0!" ) ; Guard . IsTrue ( size . Width > 0 & & size . Height > 0 , nameof ( size ) , "Source size dimensions cannot be 0!" ) ;
if ( matrix . Equals ( default ) | | matrix . Equals ( Matrix4x4 . Identity ) ) if ( matrix . IsIdentity | | matrix . Equals ( default ) )
{ {
return size ; return size ;
} }
@ -309,27 +396,7 @@ internal static class TransformUtils
// Check if the matrix involves only affine transformations by inspecting the relevant components.
// Check if the matrix involves only affine transformations by inspecting the relevant components.
// We want to use pixel space for calculations only if the transformation is purely 2D and does not include
// We want to use pixel space for calculations only if the transformation is purely 2D and does not include
// any perspective effects, non-standard scaling, or unusual translations that could distort the image.
// any perspective effects, non-standard scaling, or unusual translations that could distort the image.
// The conditions are as follows:
bool usePixelSpace = transformSpace = = TransformSpace . Pixel & & IsAffineRotationOrSkew ( matrix ) ;
bool usePixelSpace =
// 1. Ensure there's no perspective distortion:
// M34 corresponds to the perspective component. For a purely 2D affine transformation, this should be 0.
( matrix . M34 = = 0 ) & &
// 2. Ensure standard affine transformation without any unusual depth or perspective scaling:
// M44 should be 1 for a standard affine transformation. If M44 is not 1, it indicates non-standard depth
// scaling or perspective, which suggests a more complex transformation.
( matrix . M44 = = 1 ) & &
// 3. Ensure no unusual translation in the x-direction:
// M14 represents translation in the x-direction that might be part of a more complex transformation.
// For standard affine transformations, M14 should be 0.
( matrix . M14 = = 0 ) & &
// 4. Ensure no unusual translation in the y-direction:
// M24 represents translation in the y-direction that might be part of a more complex transformation.
// For standard affine transformations, M24 should be 0.
( matrix . M24 = = 0 ) ;
// Define an offset size to translate between pixel space and coordinate space.
// Define an offset size to translate between pixel space and coordinate space.
// When using pixel space, apply a scaling sensitive offset to translate to discrete pixel coordinates.
// When using pixel space, apply a scaling sensitive offset to translate to discrete pixel coordinates.
@ -376,7 +443,7 @@ internal static class TransformUtils
{ {
Guard . IsTrue ( size . Width > 0 & & size . Height > 0 , nameof ( size ) , "Source size dimensions cannot be 0!" ) ; Guard . IsTrue ( size . Width > 0 & & size . Height > 0 , nameof ( size ) , "Source size dimensions cannot be 0!" ) ;
if ( matrix . Equals ( default ) | | matrix . Equals ( Matrix3x2 . Identity ) ) if ( matrix . IsIdentity | | matrix . Equals ( default ) )
{ {
return size ; return size ;
} }
@ -412,7 +479,7 @@ internal static class TransformUtils
/// </returns>
/// </returns>
private static bool TryGetTransformedRectangle ( RectangleF rectangle , Matrix3x2 matrix , out Rectangle bounds ) private static bool TryGetTransformedRectangle ( RectangleF rectangle , Matrix3x2 matrix , out Rectangle bounds )
{ {
if ( rectangle . Equals ( default ) | | Matrix3x2 . Identity . Equals ( matrix ) ) if ( matrix . IsIdentity | | rectangle . Equals ( default ) )
{ {
bounds = default ; bounds = default ;
return false ; return false ;
@ -439,7 +506,7 @@ internal static class TransformUtils
[MethodImpl(MethodImplOptions.AggressiveInlining)] [MethodImpl(MethodImplOptions.AggressiveInlining)]
private static bool TryGetTransformedRectangle ( RectangleF rectangle , Matrix4x4 matrix , out Rectangle bounds ) private static bool TryGetTransformedRectangle ( RectangleF rectangle , Matrix4x4 matrix , out Rectangle bounds )
{ {
if ( rectangle . Equals ( default ) | | Matrix4x4 . Identity . Equals ( matrix ) ) if ( matrix . IsIdentity | | rectangle . Equals ( default ) )
{ {
bounds = default ; bounds = default ;
return false ; return false ;
@ -492,4 +559,44 @@ internal static class TransformUtils
( int ) Math . Ceiling ( right ) , ( int ) Math . Ceiling ( right ) ,
( int ) Math . Ceiling ( bottom ) ) ; ( int ) Math . Ceiling ( bottom ) ) ;
} }
private static bool IsAffineRotationOrSkew ( Matrix4x4 matrix )
{
const float epsilon = 1e-6f ;
// Check if the matrix is affine (last column should be [0, 0, 0, 1])
if ( Math . Abs ( matrix . M14 ) > epsilon | |
Math . Abs ( matrix . M24 ) > epsilon | |
Math . Abs ( matrix . M34 ) > epsilon | |
Math . Abs ( matrix . M44 - 1f ) > epsilon )
{
return false ;
}
// Translation component (M41, m42) are allowed, others are not.
if ( Math . Abs ( matrix . M43 ) > epsilon )
{
return false ;
}
// Extract the linear (rotation and skew) part of the matrix
// Upper-left 3x3 matrix
float m11 = matrix . M11 , m12 = matrix . M12 , m13 = matrix . M13 ;
float m21 = matrix . M21 , m22 = matrix . M22 , m23 = matrix . M23 ;
float m31 = matrix . M31 , m32 = matrix . M32 , m33 = matrix . M33 ;
// Compute the determinant of the linear part
float determinant = ( m11 * ( ( m22 * m33 ) - ( m23 * m32 ) ) ) -
( m12 * ( ( m21 * m33 ) - ( m23 * m31 ) ) ) +
( m13 * ( ( m21 * m32 ) - ( m22 * m31 ) ) ) ;
// Check if the determinant is approximately ±1 (no scaling)
if ( Math . Abs ( Math . Abs ( determinant ) - 1f ) > epsilon )
{
return false ;
}
// All checks passed; the matrix represents rotation and/or skew (with possible translation)
return true ;
}
} }
Ynse Hoornenborg
2 years ago
GitHub
