Question

8 Extend the transformation matrices in this lecture (scale, shear, and rotation) to 3 × 3 transformation matrices.

Extend the transformation matrices in this lecture (scale, shear, and rotation) to 3 x 3 transformation matrices.

Answer 1

Date Page No. Extend transfarma:tion Lecture(scale, shear, and rotation). the matrices in. this 3x3 transfor mation to matrices pointsin 2D Column matrix as X Y 1 Scaling of is Process of the size -changing an Limage or object Resize follosirg the in the two ways- O Minimum O Maximum bscalling ALter object 6ize factor Sx, 5y i.e = X. Sx X Sy Y = CS Scanned with CalhScanner o

Date Page No scalling_ transormation mat transformaHon matrices- extend. the to 3.x3 X Sx Y Sx x' Sy C 1 The transformahon object of Shearing shearing Skening Or applied the to wohe्x distortion iresult is. on shape shearing Y-axis X-axis Shearing factor (šhy) Shearing factor Shx) -Scarnred with CamScanner

Datend. Page No Shearing X - O y x' = x + 5hy.Y (,2) (3,2) (2, o) (0,0) (0,0) (ariginal abject). (object afterx Shear) X 1 Shx Xsn C = C Shearing AY X lonignal_object) Obiect after Y-Shea Shy 1 C shearingegiatianis, x'x y's YtShyix then the Scahned with CS CamScanner

Page No is done it such Rotation Retation Gü. as angle following directions- an the help. the in clockwise andi - clockwise/counter-clockwise O0 : Rotate ahti-clockwise <o: Rotate clockwise |ci_Anti-clockwise xotatian- anti- clockwise C Scarined witl CamScanner

Date Page No. A X = x Cos COs H y = ySin » Sin d= x' xz x Cos (+9) Cos(a+O) = _A H X Sin (p+) = D. - H equation. from fCos(A+e) x'=Cos ( 9) xx(os Cos 0- SinSin CasA COSB - SinB and xSind Sin A On puting from enO_and he value of xCos x1 - x CoS 9 - y SIn A equatian from yexSin (9 + ). Y'sxSin ) Cos 9 t x(osid Sino =F)M +Cos A Sin BI. SinA Cas B the value (x Cos )and (3 Sin ) On puting from and = x Sin O + Y Cos Ol y Sc nned with CS CamScanner 2019/6/11 16

Page fromeq and be Linal equations will XSin + Y Cos O. Sin G ) Cos & Cos & Sin & into. extended transformation matices. which be can 3 X3 Cos(e)-Sin). x'. Sine) Cosle) y' Cos (E) Sin () x' Sin(e) Cos (e) X O 1. 1 CS SHanned with GerScanneT