Transforms @qcl 2015.02.12 

No content

Transform ● Affine Transforms ○ CGAffineTransform ○ view.layer.affineTransform ● 3D Transforms ○ CATransform3D ○ view.layer.transfrom ○ view.layer.sublayerTransform 

Affine Transforms ● Math behind the matrix ○ https://developer.apple. com/library/mac/documentation/GraphicsImaging/Co nceptual/drawingwithquartz2d/dq_affine/dq_affine. html#//apple_ref/doc/uid/TP30001066-CH204- 

Affine Transforms ● Rotation ○ CGAffineTransformMakeRotation(CGFloat angle) ● Scale ○ CGAffineTransformMakeScale(CGFloat sx, CGFloat sy) ● Translation ○ CGAffineTransformMakeTranslation(CGFloat tx, CGFloat ty) 

Combining Transforms ● CGAffineTransformIdentity ○ A 3x3 Identity matrix ● Rotation ○ CGAffineTransformRotate(CGAffineTransform t, CGFloat angle) ● Scale ○ CGAffineTransformScale(CGAffineTransform t, CGFloat sx, CGFloat sy) ● Translation ○ CGAffineTransformTranslate(CGAffineTransform t, CGFloat tx, CGFloat ty) ● The order you apply transforms is important! ○ 矩陣乘法沒有交換律 

Customized Affine Transform ● You can set the fileds of a CGAffineTransform directly. ○ a ○ b ○ c ○ d ○ t x ○ t y 

3D Transforms 

3D Transforms ● Left hand coordinate system 

3D Transforms ● Rotation ○ CATransform3DMakeRotatation(CGFloat angle, CGFloat x, CGFloat y, CGFloat z) ● Scale ○ CATransform3DMakeScale(CGFloat sx, CGFloat sy, CGFloat sz) ● Translation ○ CATransform3DMakeTranslation(CGFloat tx, CGFloat ty, CGFloat tz) 

3D Transforms Combination ● CATransform3DIdentity ○ A 4x4 identity matrix ● Rotation ○ CATransform3DRotate(CATransform3D t, CGFloat angle, CGFloat x, CGFloat y, CGFloat z) ● Scale ○ CATransform3DScale(CATransform3D t, CGFloat sx, CGFloat sy, CGFloat sz) ● Translation ○ CATransform3DTranslate(CATransform3D t, CGFloat tx, CGFloat ty, CGFloat tz) 

Perspective Projection ● Prespective transform sometimes called Z transform 

Perspective Projection ● m34 of CATransform3D ● -1 / d ● More: ○ http://en.wikipedia. org/wiki/3D_projection#Perspective_projection 

Vanishing Point ● anchorPoint 

sublayerTransform ● Apply to sublayer but not affect itself. ● The vanishing point is the anchorPoint of itself, not sublayer’s anchorPoint 

Backfaces ● view.layer.doubleSided 

Layer Flattening ● Expected result is wrong. ● The layers don’t exist in the same 3D space. ● The 3D sence in each layer is flattened.