elia-mercatanti / nmg-project

Project for Numerical Methods for Graphics course. Development and implementation of some exercises based on Bézier, and B-Spline Curve or Surfaces.

Numerical Methods for Graphics Project

Project for Numerical Methods for Graphics (NMG) course. Implementation of some exercises based on Bézier Curves, B-Spline Curves and their applications on Surfaces.

Prof. Conti Part - Bezier Curves

Excercise 1

Realizes a Matlab function that implements de Casteljau algorithm for drawing Bézier Curves.

Excercise 2

Takes as input the coordinates of the control polygon and use de Casteljau algorithm to visualize the relative Bézier curve.

Excercise 3

Finds control points in the Bézier representation of the parametric with curve with equations X(t)=1+t+t^2; Y(t)=t^3 and with t in [0, 1], display the control polygon and the relative Bézier curve.

Excercise 4

Takes as input the coordinates of the control polygon of a cubic Bézier curve and use de Casteljau algorithm to perform the subdivision of the curve given a parameter t_star chosen by the user. Display the control polygons of the two divided curves and verify that continuity C^3 holds.

Excercise 5

Starting from a cubic Bézier curve defined by vertices V0, V1, V2, V3, build grade l+3 Bézier curves, with 1>=1, whose control polygon is the polygon V0, V1, V2 -- l times -- V2, V3. Shows an examples.

Excercise 6

Takes as input the coordinates of the control polygon of a cubic Bézier curve use the degree elevation algorithm to find the control polygons of this curve elevated to 4, 5, 6 degrees and draws them.

Excercise 7

Takes V0=(0,0,0), V1=(1,2,0), V2=(3,2,0), V3 =(6,-1,0) as control points of a cubic Bézier curve and builds one second cubic Bézier curve that connects with continuity C^2 with the previus curve. Display the two curves and their respective control polygons.

Prof. Giannelli Part - B-Spline Curves ans Surfaces

B-Spline Base

Takes as input the order and a knot vector to evaluate and plot all elements of the relative B-Spline base, using Cox-de Boor recursion formula.

B-Spline Closed

Close a B-Spline Curve given in input and plot the results.

B-Spline Curve - Affine Transformation

Apply some affine transformations to a B-Spline curve and plot the results.

B-Spline Curve - Variation Diminiscing

Test the variation diminiscing property of a B-Spline curve.

B-Spline Locality Property

Test the locality property of a B-Spline curve.

B-Spline Inverse Locality Property

Test the inverse locality property of a B-Spline curve.

B-Spline Surface - Affine Transformation

Apply some affine transformations to a B-Spline surface and plot the results.

B-Spline Surface Base

Plot the bases of a B-Spline surface and plot them.

B-Spline Surface - De Boor Algorithm

Plot a B-Spline surface using De Boor algorithm.

B-Spline Base - Tensor Product

Plot a B-Spline surface using tensor product.

Authors

• Elia Mercatanti
• Marco Calamai