2D仿射变换

UIView的transform属性是一个CGAffineTransform类型，用于在二维空间做旋转，缩放和平移。CGAffineTransform是一个可以和二维空间向量（例如CGPoint）做乘法的3X2的矩阵:

Paste_Image.png

当对UIView应用变换矩阵，UIView图层矩形内的每一个点都被相应地做变换，从而形成一个新的四边形的形状。CGAffineTransform中的“仿射”的意思是无论变换矩阵用什么值，图层中平行的两条线在变换之后任然保持平行.

单位矩阵

CGAffineTransformIdentity

CGAffineTransform transform = CGAffineTransformIdentity;

结果:
(CGAffineTransform) transform = (a = 1, b = 0, c = 0, d = 1, tx = 0, ty = 0)

创建仿射变换矩阵

CGAffineTransformMakeRotation(CGFloat angle)  // 旋转
CGAffineTransformMakeScale(CGFloat sx, CGFloat sy) // 缩放
CGAffineTransformMakeTranslation(CGFloat tx, CGFloat ty)  // 平移

CGAffineTransform transform = CGAffineTransformMakeRotation(M_PI_4);

结果 :
(CGAffineTransform) transform = (a = 0.70710678118654757, b = 0.70710678118654746, c = -0.70710678118654746, d = 0.70710678118654757, tx = 0, ty = 0)

CGAffineTransform transform = CGAffineTransformMakeScale(0.8, 0.8);

结果：
(CGAffineTransform) transform = (a = 0.80000000000000004, b = 0, c = 0, d = 0.80000000000000004, tx = 0, ty = 0)

CGAffineTransform transform = CGAffineTransformMakeTranslation(10, 10);

 结果：
 (CGAffineTransform) transform = (a = 1, b = 0, c = 0, d = 1, tx = 10, ty = 10)

Paste_Image.png

图中，灰色为旧图，蓝色为变化后的新图.

修改仿射变换矩阵

CGAffineTransformRotate(CGAffineTransform t, CGFloat angle) //  在矩阵t上添加旋转效果
CGAffineTransformScale(CGAffineTransform t, CGFloat sx, CGFloat sy) // 在矩阵t上添加缩放效果
CGAffineTransformTranslate(CGAffineTransform t, CGFloat tx, CGFloat ty) // 在矩阵t上添加平移效果

    //create a new transform
    CGAffineTransform transform = CGAffineTransformIdentity; 
    //scale by 50%
    transform = CGAffineTransformScale(transform, 0.5, 0.5);
    //rotate by 30 degrees
    transform = CGAffineTransformRotate(transform, M_PI / 180.0 * 30.0);
    //translate by 200 points
    transform = CGAffineTransformTranslate(transform, 200, 0);
    //apply transform to layer
    self.layerView.layer.affineTransform = transform;

https://zsisme.gitbooks.io/ios-/content/chapter5/affine-fransforms.html

3D变换

CATransform3D可以让视图在3D空间内移动或者旋转.和CGAffineTransform类似，CATransform3D也是一个矩阵，但是和2x3的矩阵不同，CATransform3D是一个可以在3维空间内做变换的4x4的矩阵.

这里讲的很好:
https://zsisme.gitbooks.io/ios-/content/chapter5/3d-transform.html
https://tech.imdada.cn/2016/06/21/ios-core-animation/