Question

Scale a triangle with vertices at original coordinates (10, 20, 5), (15,20,15), (20,10,10) by sx =2, sy =2, and sz =2 with respect to the origin. For verification, roughly plot the x and y values of the original and resultant triangles, and imagine the locations of z values​

Answer 1

Explanation:

CS3162 Introduction to Computer GraphicsHelena Wong, 200115. Three Dimensional TransformationsMethods for geometric transformations and object modelling in 3D are extended from 2D methods by including the considerations for the z coordinate.Basic geometric transformations are: Translation, Rotation, Scaling 5.1 Basic TransformationsTranslationWe translate a 3D point by adding translation distances, tx, ty, and tz, to the original coordinate position (x,y,z):x' = x + tx, y' = y + ty, z' = z + tzAlternatively, translation can also be specified by the transformation matrix in the following formula:1'z'y'x=1000t100t010t001zyx1zyxExercise: translate a triangle with vertices at original coordinates (10,25,5), (5,10,5), (20,10,10) by tx=15, ty=5,tz=5. For verification, roughly plot the x and y values of the original and resultant triangles, and imagine the locations of z values.Scaling With Respect to the OriginWe scale a 3D object with respect to the origin by setting the scaling factors sx, sy and sz, which are multiplied to the original vertex coordinate positions (x,y,z):x' = x * sx, y' = y * sy, z' = z * szAlternatively, this scaling can also be specified by the transformation matrix in the following formula:1'z'y'x=10000s0000s0000szyx1zyxExercise: Scale a triangle with vertices at original coordinates (10,25,5), (5,10,5), (20,10,10) by sx=1.5, sy=2, and sz=0.5 with respect to the origin. For verification, roughly plot the x and y values of the original and resultant triangles, and imagine the locations of z values.Scaling with respect to a Selected Fixed PositionExercise: What are the steps to perform scaling with respect to a selected fixed position? Check your answer with the text book.Exercise: Scale a triangle with vertices at original coordinates (10,25,5), (5,10,5), (20,10,10) by sx=1.5, sy=2, and sz=0.5 with respect to the centre of the triangle. For verification, roughly plot the x and y values of the original and resultant triangles, and imagine the locations of z values.