CGAffineTransform

struct CGAffineTransform {
  CGFloat a, b, c, d;
  CGFloat tx, ty;
};

/* The identity transform: [ 1 0 0 1 0 0 ]. */

CG_EXTERN const CGAffineTransform CGAffineTransformIdentity
  CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformMake(CGFloat a, CGFloat b,
  CGFloat c, CGFloat d, CGFloat tx, CGFloat ty)
  CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformMakeTranslation(CGFloat tx,
  CGFloat ty) CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformMakeScale(CGFloat sx, CGFloat sy)
  CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformMakeRotation(CGFloat angle)
  CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN bool CGAffineTransformIsIdentity(CGAffineTransform t)
  CG_AVAILABLE_STARTING(__MAC_10_4, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformTranslate(CGAffineTransform t,
  CGFloat tx, CGFloat ty) CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformScale(CGAffineTransform t,
  CGFloat sx, CGFloat sy) CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformRotate(CGAffineTransform t,
  CGFloat angle) CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformInvert(CGAffineTransform t)
  CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGAffineTransform CGAffineTransformConcat(CGAffineTransform t1,
  CGAffineTransform t2) CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN bool CGAffineTransformEqualToTransform(CGAffineTransform t1,
  CGAffineTransform t2) CG_AVAILABLE_STARTING(__MAC_10_4, __IPHONE_2_0);

CG_EXTERN CGPoint CGPointApplyAffineTransform(CGPoint point,
  CGAffineTransform t) CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGSize CGSizeApplyAffineTransform(CGSize size, CGAffineTransform t)
  CG_AVAILABLE_STARTING(__MAC_10_0, __IPHONE_2_0);

CG_EXTERN CGRect CGRectApplyAffineTransform(CGRect rect, CGAffineTransform t)
  CG_AVAILABLE_STARTING(__MAC_10_4, __IPHONE_2_0);

CG_INLINE CGAffineTransform
__CGAffineTransformMake(CGFloat a, CGFloat b, CGFloat c, CGFloat d,
  CGFloat tx, CGFloat ty)
{
  CGAffineTransform t;
  t.a = a; t.b = b; t.c = c; t.d = d; t.tx = tx; t.ty = ty;
  return t;
}

CG_INLINE CGPoint
__CGPointApplyAffineTransform(CGPoint point, CGAffineTransform t)
{
  CGPoint p;
  p.x = (CGFloat)((double)t.a * point.x + (double)t.c * point.y + t.tx);
  p.y = (CGFloat)((double)t.b * point.x + (double)t.d * point.y + t.ty);
  return p;
}

CG_INLINE CGSize
__CGSizeApplyAffineTransform(CGSize size, CGAffineTransform t)
{
  CGSize s;
  s.width = (CGFloat)((double)t.a * size.width + (double)t.c * size.height);
  s.height = (CGFloat)((double)t.b * size.width + (double)t.d * size.height);
  return s;
}