【学Rust写CAD】17 通用2D仿射变换矩阵结构体（matrix/generic.rs）

源代码

// matrix.rs
use std::ops::{Add, Mul};use std::ops::{Add, Mul};/// 通用2D仿射变换矩阵（元素仅需Copy）
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct Matrix<X, Y, Xx, Xy, Yx, Yy> {pub x: X, pub y: Y,pub xx: Xx, pub xy: Xy,pub yx: Yx, pub yy: Yy,
}impl<X, Y, Xx, Xy, Yx, Yy> Matrix<X, Y, Xx, Xy, Yx, Yy> {/// 通用二元运算接口#[inline]fn binary_op<A, B, C, D, O>(a: A, b: B, c: C, d: D) -> OwhereO: From<(A, B, C, D)>{O::from((a, b, c, d))}
}/// 线性组合运算转换器
pub struct LinearCombination<A, B, C, D>(pub A, pub B, pub C, pub D);impl<A, B, C, D> From<(A, B, C, D)> for LinearCombination<A, B, C, D> {fn from(t: (A, B, C, D)) -> Self {LinearCombination(t.0, t.1, t.2, t.3)}
}impl<A, B, C, D, AB, CD> From<LinearCombination<A, B, C, D>> for <AB as Add<CD>>::Output
whereA: Mul<B, Output = AB>,C: Mul<D, Output = CD>,AB: Add<CD>
{fn from(lc: LinearCombination<A, B, C, D>) -> Self {lc.0 * lc.1 + lc.2 * lc.3}
}impl<X1, Y1, Xx1, Xy1, Yx1, Yy1,X2, Y2, Xx2, Xy2, Yx2, Yy2,
> Mul<Matrix<X2, Y2, Xx2, Xy2, Yx2, Yy2>> for Matrix<X1, Y1, Xx1, Xy1, Yx1, Yy1>
where// 基础约束（仅Copy）X1: Copy, Y1: Copy, Xx1: Copy, Xy1: Copy, Yx1: Copy, Yy1: Copy,X2: Copy, Y2: Copy, Xx2: Copy, Xy2: Copy, Yx2: Copy, Yy2: Copy,// 平移运算约束（不限制Output类型）Xx2: Mul<X1>,Xy2: Mul<Y1>,Yx2: Mul<X1>,Yy2: Mul<Y1>,// 线性变换约束（不限制Output类型）Xx1: Mul<Xx2>,Xx1: Mul<Yx2>,Xy1: Mul<Xy2>,Xy1: Mul<Yy2>,Yx1: Mul<Xx2>,Yx1: Mul<Yx2>,Yy1: Mul<Xy2>,Yy1: Mul<Yy2>,// 加法约束（自动推导）<Xx1 as Mul<Xx2>>::Output: Add<<Xy1 as Mul<Yx2>>::Output>,<Xx1 as Mul<Xy2>>::Output: Add<<Xy1 as Mul<Yy2>>::Output>,<Yx1 as Mul<Xx2>>::Output: Add<<Yy1 as Mul<Yx2>>::Output>,<Yx1 as Mul<Xy2>>::Output: Add<<Yy1 as Mul<Yy2>>::Output>,
{type Output = Matrix<<X1 as Add<<Xx2 as Mul<X1>>::Output>>::Output,  // X<Y1 as Add<<Yy2 as Mul<Y1>>::Output>>::Output,  // Y<<Xx1 as Mul<Xx2>>::Output as Add<<Xy1 as Mul<Yx2>>::Output>>::Output, // Xx<<Xx1 as Mul<Xy2>>::Output as Add<<Xy1 as Mul<Yy2>>::Output>>::Output, // Xy<<Yx1 as Mul<Xx2>>::Output as Add<<Yy1 as Mul<Yx2>>::Output>>::Output, // Yx<<Yx1 as Mul<Xy2>>::Output as Add<<Yy1 as Mul<Yy2>>::Output>>::Output  // Yy>;fn mul(self, rhs: Matrix<X2, Y2, Xx2, Xy2, Yx2, Yy2>) -> Self::Output {Matrix {// 平移计算（完全自由类型推导）x: self.x + rhs.x * self.xx + rhs.y * self.yx,y: self.y + rhs.x * self.xy + rhs.y * self.yy,// 通过转换器计算线性变换xx: Self::binary_op::<_, _, _, _, _>(self.xx, rhs.xx, self.xy, rhs.yx),xy: Self::binary_op::<_, _, _, _, _>(self.xx, rhs.xy, self.xy, rhs.yy),yx: Self::binary_op::<_, _, _, _, _>(self.yx, rhs.xx, self.yy, rhs.yx),yy: Self::binary_op::<_, _, _, _, _>(self.yx, rhs.xy, self.yy, rhs.yy),}}
}

代码分析

矩阵布局
矩阵采用以下布局：

$\begin{bmatrix}1 & x & y \\ 0 & xx & xy \\ 0 & yx & yy \end{bmatrix}$

这种布局的特点是：

平移分量 x 和 y 位于第一行
线性变换部分位于右下2x2子矩阵
左下保持 [0, 0] 以保证是仿射变换

核心功能
矩阵乘法
两个矩阵相乘的结果计算如下：

$\begin{bmatrix}1 & x1 & y1 \\ 0 & xx1 & xy1 \\ 0 & yx1 & yy1 \end{bmatrix} * \begin{bmatrix}1 & x2 & y2 \\ 0 & xx2 & xy2 \\ 0 & yx2 & yy2 \end{bmatrix}= \begin{bmatrix}1 & x1+x2*xx1+y2*yx1 & y1+x2*xy1+y2*yy1 \\ 0 & xx1*xx2+xy1*yx2 & xx1*xy2+xy1*yy2 \\ 0 & yx1*xx2+yy1*yx2 & yx1*xy2+yy1*yy2 \end{bmatrix}$