CoreAnimation-CGAffineTransform

#define M_E2.71828182845904523536028747135266250e
#define M_LOG2E1.44269504088896340735992468100189214log 2e
#define M_LOG10E0.434294481903251827651128918916605082log 10e
#define M_LN20.693147180559945309417232121458176568log e2
#define M_LN102.30258509299404568401799145468436421log e10
#define M_PI3.14159265358979323846264338327950288pi
#define M_PI_21.57079632679489661923132169163975144pi/2
#define M_PI_40.785398163397448309615660845819875721pi/4
#define M_1_PI0.3183098861837906715377675267450287241/pi
#define M_2_PI0.6366197723675813430755350534900574482/pi
#define M_2_SQRTPI1.128379167095512573896158903121545172/sqrt(pi)
#define M_SQRT21.41421356237309504880168872420969808sqrt(2)

#define M_SQRT1_20.7071067811865475244008443621048490391/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