Vectors and Matrices

259.353 Themengebiete der algorithmischen Planung und Analyse. SS2013
Vienna University of Technology; TISS: VO, 259.353

Matrices Operations
Point A:
Point B:
Point C:
Point D:
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rotation

matrix:
angle:
 

calculation

Ax1= cos(a)*Ax - sin(a)*Ay
Ax1= * - * =
Ay1= sin(a)*Ax + cos(a)*Ay
Ay1= * + * =
Bx1= * - * =
By1= * + * =

reflection

matrix:
Point G:
 

calculation

k= Gy/Gx = / =
a= atan(k)=
Ax1= cos(2a)*Ax + sin(2a)*Ay
Ax1= * + * =
Ay1= sin(2a)*Ax - cos(2a)*Ay
Ay1= * - * =
Bx1= * + * =
By1= * - * =

dilation

matrix:
dilation factor:
 

calculation

Ax1= c*Ax
Ax1= * =
Ay1= c*Ay
Ay1= * =
Bx1= * =
By1= * =
angle:

rotation & dilation

dilation factor:

dilation & rotation

angle:

rotation & dilation

Point G:

dilation & rotation

general

matrix:

a11
a12
a21
a22
 

calculation

Ax1= a11*Ax + a21*Ay
Ax1= * + * =
Ay1= a12*Ax + a22*Ay
Ay1= * + * =

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