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MoSiG, Computer Graphics II

Geometric Modeling

Homework

Due:

Tuesday, November 6, 2018

Send email to Georges-Pierre.Bonneau at inria.fr with archive containing pdf report and program sources

Email object: [MOSIG] CGII

Send email to Georges-Pierre.Bonneau at inria.fr with archive containing pdf report and program sources

Email object: [MOSIG] CGII

Objective:

Implement basic curve subdivision schemes

Illustrate their convergence

Illustrate their convergence

Download starting source code: MOSIG_CGII_FOR_STUDENTS

A Subdivision Curve

Its Curvature Plot: the curve is NOT C2

TODO

1) Implement for an arbitrary closed polygon the following curve subdivision scheme:

a. Chaikin

b. Corner cutting (with parameters a and b)

c. 4-point scheme

d. Generalized 4-point scheme

e. Uniform splines of degree 3

b. Corner cutting (with parameters a and b)

c. 4-point scheme

d. Generalized 4-point scheme

e. Uniform splines of degree 3

2) Compute a distance between a given polygon and its subdivision

3) Compute the angles at each vertices of a closed polygon

4) Write a short report (max 4 to 5 pages including illustrations), with illustration of the implemented subdivision schemes, together with plots showing the convergence of the scheme and the smoothness (C0, C1 or C2) of the limit