简记:
CGAffineTransformMake(a,b,c,d,tx,ty)
ad缩放bc旋转tx,ty位移，基础的2D矩阵
公式
x=ax+cy+tx
y=bx+dy+ty
1.矩阵的基本知识：
struct CGAffineTransform
{
CGFloat a, b, c, d;
CGFloat tx, ty;
};
CGAffineTransform CGAffineTransformMake (CGFloat a,CGFloat b,CGFloat c,CGFloat d,CGFloat tx,CGFloat ty);
为了把二维图形的变化统一在一个坐标系里，引入了齐次坐标的概念，即把一个图形用一个三维矩阵表示，其中第三列总是(0,0,1)，用来作为坐标系的标准。所以所有的变化都由前两列完成。
以上参数在矩阵中的表示为：
|a b 0|
|c d 0|
|tx ty 1|
运算原理：原坐标设为（X,Y,1）;
|a b 0|
[X，Y, 1] |c d 0| = [aX + cY + tx bX + dY + ty 1] ;
|tx ty 1|
通过矩阵运算后的坐标[aX + cY + tx bX + dY + ty 1]，我们对比一下可知：
第一种：设a=d=1, b=c=0.
[aX + cY + tx bX + dY + ty 1] = [X + tx Y + ty 1];
可见，这个时候，坐标是按照向量（tx，ty）进行平移，其实这也就是函数
CGAffineTransform CGAffineMakeTranslation(CGFloat tx,CGFloat ty)的计算原理。
第二种：设b=c=tx=ty=0.
[aX + cY + tx bX + dY + ty 1] = [aX dY 1];
可见，这个时候，坐标X按照a进行缩放，Y按照d进行缩放，a，d就是X，Y的比例系数，其实这也就是函数
CGAffineTransform CGAffineTransformMakeScale(CGFloat sx, CGFloat sy)的计算原理。a对应于sx，d对应于sy。
第三种：设tx=ty=0，a=cosɵ，b=sinɵ，c=-sinɵ，d=cosɵ。
[aX + cY + tx bX + dY + ty 1] = [Xcosɵ - Ysinɵ Xsinɵ + Ycosɵ 1] ;
可见，这个时候，ɵ就是旋转的角度，逆时针为正，顺时针为负。其实这也就是函数
CGAffineTransform CGAffineTransformMakeRotation(CGFloat angle)的计算原理。angle即ɵ的弧度表示。
2.利用上面的变换写一个UIImage矩阵变换的例子：
下面是一个关于image的矩阵运算的例子,无外乎是运用以上三种变换的组合，达到所定义的效果
//UIImageOrientation的定义，定义了如下几种变换
typedef enum
{
UIImageOrientationUp, // default orientation
UIImageOrientationDown, // 180 deg rotation
UIImageOrientationLeft, // 90 deg CCW
UIImageOrientationRight, // 90 deg CW
UIImageOrientationUpMirrored, // as above but image mirrored along other axis. horizontal flip
UIImageOrientationDownMirrored, // horizontal flip
UIImageOrientationLeftMirrored, // vertical flip
UIImageOrientationRightMirrored, // vertical flip
} UIImageOrientation;
//按照UIImageOrientation的定义，利用矩阵自定义实现对应的变换；
-(UIImage *)transformImage:(UIImage *)aImage
{
CGImageRef imgRef = aImage.CGImage;
CGFloat width = CGImageGetWidth(imgRef);
CGFloat height = CGImageGetHeight(imgRef);
CGAffineTransform transform = CGAffineTransformIdentity;
CGRect bounds = CGRectMake(0, 0, width, height);
CGFloat scaleRatio = 1;
CGFloat boundHeight;
UIImageOrientation orient = aImage.imageOrientation;
switch(UIImageOrientationLeftMirrored)
{
case UIImageOrientationUp:
transform = CGAffineTransformIdentity;
break;
case UIImageOrientationUpMirrored:
transform = CGAffineTransformMakeTranslation(width, 0.0);
transform = CGAffineTransformScale(transform, -1.0, 1.0); //沿y轴向左翻
break;
case UIImageOrientationDown:
transform = CGAffineTransformMakeTranslation(width, height);
transform = CGAffineTransformRotate(transform, M_PI);
break;
case UIImageOrientationDownMirrored:
transform = CGAffineTransformMakeTranslation(0.0, height);
transform = CGAffineTransformScale(transform, 1.0, -1.0);
break;
case UIImageOrientationLeft:
boundHeight = bounds.size.height;
bounds.size.height = bounds.size.width;
bounds.size.width = boundHeight;
transform = CGAffineTransformMakeTranslation(0.0, width);
transform = CGAffineTransformRotate(transform, 3.0 * M_PI / 2.0);
break;
case UIImageOrientationLeftMirrored:
boundHeight = bounds.size.height;
bounds.size.height = bounds.size.width;
bounds.size.width = boundHeight;
transform = CGAffineTransformMakeTranslation(height, width);
transform = CGAffineTransformScale(transform, -1.0, 1.0);
transform = CGAffineTransformRotate(transform, 3.0 * M_PI / 2.0);
break;
case UIImageOrientationRight: //EXIF = 8
boundHeight = bounds.size.height;
bounds.size.height = bounds.size.width;
bounds.size.width = boundHeight;
transform = CGAffineTransformMakeTranslation(height, 0.0);
transform = CGAffineTransformRotate(transform, M_PI / 2.0);
break;
case UIImageOrientationRightMirrored:
boundHeight = bounds.size.height;
bounds.size.height = bounds.size.width;
bounds.size.width = boundHeight;
transform = CGAffineTransformMakeScale(-1.0, 1.0);
transform = CGAffineTransformRotate(transform, M_PI / 2.0);
break;
default:
[NSException raise:NSInternalInconsistencyException format:@"Invalid image orientation"];
}
UIGraphicsBeginImageContext(bounds.size);
CGContextRef context = UIGraphicsGetCurrentContext();
if (orient == UIImageOrientationRight || orient == UIImageOrientationLeft) {
CGContextScaleCTM(context, -scaleRatio, scaleRatio);
CGContextTranslateCTM(context, -height, 0);
}
else {
CGContextScaleCTM(context, scaleRatio, -scaleRatio);
CGContextTranslateCTM(context, 0, -height);
}
CGContextConcatCTM(context, transform);
CGContextDrawImage(UIGraphicsGetCurrentContext(), CGRectMake(0, 0, width, height), imgRef);
UIImage *imageCopy = UIGraphicsGetImageFromCurrentImageContext();
UIGraphicsEndImageContext();
return imageCopy;
}
参考：
https://developer.apple.com/library/ios/documentation/GraphicsImaging/Conceptual/drawingwithquartz2d/dq_affine/dq_affine.html