Computer Graphics with Open GL

Donald Hearn. M. Pauline. Baker, Warren R.Carithers

Chapter 8 Three-Dimensional Geometric Transformations - all with Video Answers

Educators

Chapter Questions

03:02

Problem 1

Show that rotation matrix 33 is equal to the composite matrix $\mathbf{R}_{y}(\beta) \cdot \mathbf{R}_{x}(\alpha)$.

Muhammad Saleem

Numerade Educator

01:07

Problem 2

By evaluating the terms in Equation 37 , derive the elements for the general rotation matrix given in Equation 38 .

Raj Bala

Numerade Educator

01:07

Problem 3

Prove that the quaternion rotation matrix 38 reduces to the matrix representation in Equation 5 when the rotation axis is the coordinate $z$ axis.

Raj Bala

Numerade Educator

02:34

Problem 4

Prove that Equation 40 is equivalent to the general rotation transformation given in Equation 28 .

Ashley Boni

Numerade Educator

08:30

Problem 5

Using trigonometric identities, derive the elements of the quaternion-rotation matrix 39 from 38 .

Melissa Munoz

Numerade Educator

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Develop a procedure for animating a threedimensional object by incrementally rotating it about any specified axis. Use appropriate approximations to the trigonometric equations to speed up the calculations, and reset the object to its initial position after each complete revolution about the axis.

Lainey Roebuck

Numerade Educator

03:50

Problem 7

Derive the three-dimensional transformation matrix for scaling an object by a scaling factor $s$ in a direction defined by the direction cosines $\alpha, \beta$, and $\gamma$.

William Dunkerton

Numerade Educator

01:23

Problem 8

Develop a routine to reflect a three-dimensional object about an arbitrarily selected plane.

Himanshu Kushwaha

Numerade Educator

01:56

Problem 9

Write a procedure to shear a three-dimensional object with respect to any specified axis, using input values for the shearing parameters.

Surendra Kumar

Numerade Educator

01:14

Problem 10

Develop a procedure for converting an object definition in one three-dimensional coordinate reference to any other coordinate system defined relative to the first system.