CoreAnimation-CGAffineTransform

#define M_E         2.71828182845904523536028747135266250   e
#define M_LOG2E     1.44269504088896340735992468100189214   log 2e
#define M_LOG10E    0.434294481903251827651128918916605082  log 10e
#define M_LN2       0.693147180559945309417232121458176568  log e2
#define M_LN10      2.30258509299404568401799145468436421   log e10
#define M_PI        3.14159265358979323846264338327950288   pi
#define M_PI_2      1.57079632679489661923132169163975144   pi/2
#define M_PI_4      0.785398163397448309615660845819875721  pi/4
#define M_1_PI      0.318309886183790671537767526745028724  1/pi
#define M_2_PI      0.636619772367581343075535053490057448  2/pi
#define M_2_SQRTPI  1.12837916709551257389615890312154517   2/sqrt(pi)
#define M_SQRT2     1.41421356237309504880168872420969808   sqrt(2)

#define M_SQRT1_2   0.707106781186547524400844362104849039  1/sqrt(2)

Quartz提供的3大功能

移动，旋转，缩放

演示如下，首先加载一张图片

void CGContextDrawImage (    CGContextRef c,    CGRect rect,    CGImageRef image );
 
 
移动函数
CGContextTranslateCTM (myContext, 100, 50);

旋转函数

include <math.h> static inline double radians (double degrees) {return degrees * M_PI/180;}

CGContextRotateCTM (myContext, radians(–45.));


缩放
CGContextScaleCTM (myContext, .5, .75);


翻转， 两种转换合成后的效果，先把图片移动到右上角，然后旋转180度
CGContextTranslateCTM (myContext, w,h); CGContextRotateCTM (myContext, radians(-180.));
组合几个动作
CGContextTranslateCTM (myContext, w/4, 0); CGContextScaleCTM (myContext, .25,  .5); CGContextRotateCTM (myContext, radians ( 22.));
 
CGContextRotateCTM (myContext, radians ( 22.)); CGContextScaleCTM (myContext, .25,  .5);
CGContextTranslateCTM (myContext, w/4, 0);

上面是通过直接修改当前的ctm实现3大效果，下面是通过创建Affine Transforms，然后连接ctm实现同样的3种效果
这样做的好处是可以重用这个Affine Transforms
应用Affine Transforms 到ctm的函数
void CGContextConcatCTM (    CGContextRef c,    CGAffineTransform transform );
Creating Affine Transforms
移动效果
CGAffineTransform CGAffineTransformMakeTranslation (    CGFloat tx,    CGFloat ty );
CGAffineTransform CGAffineTransformTranslate (    CGAffineTransform t,    CGFloat tx,    CGFloat ty );
旋转效果
CGAffineTransform CGAffineTransformMakeRotation (    CGFloat angle );
CGAffineTransform CGAffineTransformRotate (    CGAffineTransform t,    CGFloat angle );
缩放效果
CGAffineTransform CGAffineTransformMakeScale (    CGFloat sx,    CGFloat sy );
CGAffineTransform CGAffineTransformScale (    CGAffineTransform t,    CGFloat sx,    CGFloat sy );
反转效果
CGAffineTransform CGAffineTransformInvert (    CGAffineTransform t );
只对局部产生效果
CGRect CGRectApplyAffineTransform (    CGRect rect,    CGAffineTransform t );
判断两个AffineTrans是否相等
bool CGAffineTransformEqualToTransform (    CGAffineTransform t1,    CGAffineTransform t2 );
获得Affine Transform
CGAffineTransform CGContextGetUserSpaceToDeviceSpaceTransform (    CGContextRef c );
下面的函数只起到查看的效果，比如看一下这个用户空间的点，转换到设备空间去坐标是多少
CGPoint CGContextConvertPointToDeviceSpace (    CGContextRef c,    CGPoint point );
CGPoint CGContextConvertPointToUserSpace (    CGContextRef c,    CGPoint point );
CGSize CGContextConvertSizeToDeviceSpace (    CGContextRef c,    CGSize size );
CGSize CGContextConvertSizeToUserSpace (    CGContextRef c,    CGSize size );
CGRect CGContextConvertRectToDeviceSpace (    CGContextRef c,    CGRect rect );
CGRect CGContextConvertRectToUserSpace (    CGContextRef c,    CGRect rect );
CTM真正的数学行为
这个转换矩阵其实是一个 3x3的 举证
如下图
下面举例说明几个转换运算的数学实现
x y 是原先点的坐标
下面是从用户坐标转换到设备坐标的计算公式
下面是一个identity matrix，就是输入什么坐标，出来什么坐标，没有转换
最终的计算结果是 x=x，y=y，  
 可以用函数判断这个矩阵是不是一个 identity matrix
bool CGAffineTransformIsIdentity (    CGAffineTransform t );
移动矩阵
 
缩放矩阵
 
旋转矩阵
 
旋转加移动矩阵
 
 
参考：http://developer.apple.com/iphone/library/documentation/GraphicsImaging/Conceptual/drawingwithquartz2d/dq_affine/dq_affine.html#//apple_ref/doc/uid/TP30001066-CH204-SW1