Matrix transformations in iOS development

Recently in the study Coretext read a lot of examples of which many of them are not specifically understood so the internet collected the iOS matrix conversion principle to record

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Cgaffinetransformmake (A,b,c,d,tx,ty)

Ad scaling BC rotational tx,ty displacement, base 2D matrix

Formula

X=ax+cy+tx
Y=bx+dy+ty

1. Basic knowledge of matrices:

struct Cgaffinetransform

{
CGFloat A, B, C, D;
CGFloat tx, Ty;
};

Cgaffinetransform Cgaffinetransformmake (CGFloat a,cgfloat b,cgfloat c,cgfloat d,cgfloat tx,cgfloat ty);

In order to unify the change of the two-dimensional graph in a coordinate system, the concept of homogeneous coordinates is introduced, that is, a graph is represented by a three-dimensional matrix, where the third column is always (0,0,1) and used as the standard of coordinate system. so all the changes are done by the first two columns.

The above parameters are represented in the matrix as:

|a b 0|

|c D 0|

|tx Ty 1|

Operation principle: The original coordinates are set to (x,y,1);

|a b 0|

[X, Y, 1] |c d 0| = [AX + CY + tx BX + DY + ty 1];

|tx Ty 1|

After the matrix operation coordinates [AX + CY + tx BX + DY + ty 1], let's compare the following:

The first kind: set a=d=1, b=c=0.

[AX + CY + tx BX + DY + ty 1] = [X + tx Y + ty 1];

Visible, at this time, coordinates are translated according to the Vector (Tx,ty), which is actually the function

The computational principle of Cgaffinetransform cgaffinemaketranslation (cgfloat tx,cgfloat ty).

The second type: set b=c=tx=ty=0.

[ax + CY + tx BX + DY + ty 1] = [ax-dy 1];

Visible, at this time, coordinates x is scaled according to a, Y is scaled by D, a,d is the scale factor of x, Y, which is actually the function

Cgaffinetransform Cgaffinetransformmakescale (cgfloat sx, cgfloat sy) Calculation principle. A corresponds to the sx,d corresponding to the SY.

The Third Kind: set Tx=ty=0,a=cos?,b=sin?,c=-sin?,d=cos?

[AX + CY + tx BX + DY + ty 1] = [Xcos?-Ysin? Xsin?  + Ycos? 1];

Visible, this time, is the angle of rotation, counterclockwise is positive, clockwise is negative. Actually, that's the function.

Cgaffinetransform cgaffinetransformmakerotation (cgfloat angle) calculation principle. The radian of angle is.

Matrix transformations in iOS development