Geometric functions in computer aided geometric design by Oscar Ruiz

Author:Oscar Ruiz
Language: spa
Format: epub
Publisher: Universidad EAFIT
Published: 2020-10-14T16:00:00+00:00

Notice that the associativity property (Equation 4.22) does not depend on Mi being rigid transformations.

2. The equation Sn = M * S0 directly allows to calculate M without following a particular transformation sequence.

4.4.4 Proposed Exercises. Rotations about Main Axis

1. Prove that is invertible iff S0 is a Coordinate System for R3.

2. Assume a sequence of (not necessarily rigid) transformations M = Mn * Mn−1 * ...* M1 applied onto S0 to produce Sn. In reduced way,

(a) Prove that using Equation 4.23 to find M requires that is invertible. Under which conditions is S0 invertible?

(b) Assume in Equation 4.23 that S0 is invertible. Can M be found if Sn is not invertible? What is the effect on M of Sn being non-invertible?

(c) Prove using Equation 4.23 that assuming that S0 is RHCCS, then M is rigid ⇔ Sn is a RHCCS.

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