Add QuadDistortion to ProjectiveTransformBuilder

[Socolin]

Prerequisites

• [x] I have written a descriptive pull-request title
• [x] I have verified that there are no overlapping pull-requests open
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• [x] I have provided test coverage for my change (where applicable)

Description

Add 2 new methods: PrependQuadDistortion and AppendQuadDistortion to ProjectiveTransformBuilder.

Those method allow to apply a distortion on an image by specifying the requested coordinate for each corner.

Example:

using (var img1 = Image.Load("cat-original.png"))
{
	var topLeft = new Point(25, 25);
	var topRight = new Point(200, 75);
	var bottomRight = new Point(225, 175);
	var bottomLeft = new Point(38, 225);

	img1.Mutate(c => c.Transform(new ProjectiveTransformBuilder()
		.AppendQuadDistort(topLeft, topRight, bottomRight, bottomLeft)));
	img1.Save("output-small2.png");
}

Source Result

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[JimBobSquarePants]

Thanks @Socolin for this, it is very interesting! I'll have to put my math's hat on to look at this.

I'm curious. Is this potentially an alternative (better) approach to ProjectiveTransformBuilder.PrependTaper?

[Socolin]

FYI: The performance test I did

TestPerformanceGaussianElimination.zip

• Matrix is using MathNet.Numerics Nuget
• MatrixCustom is the implementation included in this PR
• MatrixCustomFloat is the same implementation with float instead of a generic
• Matrix8x8 is using TNumber[,] instead of TNumber[][] with static size of 8x8

BenchmarkDotNet v0.13.12, Ubuntu 22.04.4 LTS (Jammy Jellyfish)
AMD Ryzen 9 7950X, 1 CPU, 32 logical and 16 physical cores
.NET SDK 8.0.302
  [Host]     : .NET 8.0.6 (8.0.624.26715), X64 RyuJIT AVX-512F+CD+BW+DQ+VL+VBMI
  DefaultJob : .NET 8.0.6 (8.0.624.26715), X64 RyuJIT AVX-512F+CD+BW+DQ+VL+VBMI


| Method            | Mean     | Error   | StdDev  |
|------------------ |---------:|--------:|--------:|
| Matrix            | 526.6 ns | 1.02 ns | 0.96 ns |
| MatrixCustom      | 237.0 ns | 3.31 ns | 3.09 ns |
| MatrixCustomFloat | 234.1 ns | 4.64 ns | 4.34 ns |
| Matrix8x8         | 293.5 ns | 0.32 ns | 0.28 ns |

[JimBobSquarePants]

@Socolin I'll see if I can find some time over the next few days to pull down your fork and help reimplement it into the latest codebase. I'm keen to add this functionality.

[Socolin]

@Socolin I'll see if I can find some time over the next few days to pull down your fork and help reimplement it into the latest codebase. I'm keen to add this functionality.

I finally have some time again. I'll push changes related to the today. If it's easier for you to take over this PR, feel free to do it :)

[Socolin]

I rebased the branch and pushed the changes

[Socolin]

I just saw I'm getting an error because ProjectiveTransformBuilder Append take 2 arguments now, should this be computed twice ? Since this operation is taking some processing time, I'm not sure about what to do here.

[JimBobSquarePants]

I just saw I'm getting an error because ProjectiveTransformBuilder Append take 2 arguments now, should this be computed twice ? Since this operation is taking some processing time, I'm not sure about what to do here.

The operation takes nanoseconds so I'm not concerned by that.

[JimBobSquarePants]

Hi @Socolin would it be possible for you to give me full write access to your fork so I can complete this PR for you?

There's a known issue with Git LFS and GitHub which means I cannot update the reference images without full write access.

Thanks!

[Socolin]

I did grant you access to the repo, can you confirm it's all right ?

[JimBobSquarePants]

I did grant you access to the repo, can you confirm it's all right ?

Perfect. Thank you!

[JimBobSquarePants]

I think this is good to go now. Thanks @Socolin for submitting the solution for this. It's a fantastic addition to the library!