Programming Assignment 3 (Due date extended - Oct 26th Tuesday)

Evaluating B-Spline Surfaces

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General

This assignment implements code to evaluate a B-Spline surface in order to render it. Most graphics systems render surfaces by tesselating them. We will do this by evaluating a number of points on the surface and using these points to output triangles. Since this is not a programming course you may choose the language, but you should not use build-in functions in Matlab/Mathematica or other packages to render the B-Spline surface directly. Tesselat the surface and output the triangles instead.

Your program should accomplish the following:

Allow the user to enter several data points which will be displayed on the screen.
Generate a uniform cubic B-Spline surface through these points.
You should make up input files consisting of surfaces, and the resulting output files of triangles on the surface to make the following shapes:

One tensor product cubic B-Spline blending function. ie Q(u,v) = ( u, v, B_(3,3)(u,v) )
A cylinder
A torus
A cube
A triangular patch
A closed ball

Code

You may program in any language, although Matlab is recommended. If your program is in a language other than Matlab, Mathematica, C/C++, or Java, I may ask you to demonstrate it.
Any package can be used for the viewing purpose. You should not use build-in functions in Matlab, Mathematica, or other packages for generating B-Spline surfaces.
Your code should be readable. The first part of every function should contain a block of comments that give a detailed description of the code's purpose, usage, and its input and output variables.
Your code should return warning and error messages for invalid input data.

Input/Output

All values in the following descriptions are floating point, unless preceded by int.

The input will consist of a file in the following form:

(int) Number of Surfaces u step size v step size

(int) Number of control points along each row in first surface
(int) Number of control points along each column in first surface

first control point in first row x
first control point in first row y
first control point in first row z
second control point in first row x
second control point in first row y
second control point in first row z
...
last control point in first row x
last control point in first row y
last control point in first row z
...
first control point in second row x
first control point in second row y
first control point in second row z
...
last control point in last row x
last control point in last row y
last control point in last row z

(int) Number of control points along each row in second surface
(int) Number of control points along each column in second surface

_{...
... ...

... ... ...}

(int) Number of control points along each row in last surface
(int) Number of control points along each column in last surface

The output will be a file of triangles in the following form:

(int) Number of triangles

x₀₀ y₀₀z₀₀

x₀₁ y₀₁ z₀₁

x₀₂ y₀₂z₀₂

x₁₀ y₁₀z₁₀

x₁₁ y₁₁ z₁₁

x₁₂ y₁₂z₁₂

_{... ...
...}

x_n0 y_n0z_n0

x_n1 y_n1 z_n1

x_n2 y_n2z_n2

Where "x_ij y_ij z_ij" means i^th triangle's j^th vertex.

A simple example of the output file format with four triangles arranged in a rough tetrahedron:

4
-1 -1 1
1 -1 1
0 1 0
0 -1 -1
-1 -1 1
0 1 0
1 -1 1
0 -1 -1
0 1 0
-1 -1 1
0 -1 -1
1 -1 1

The output should be generated by evaluating each surface patch at parameter values incremented by u step size in u and v step size in v. The triangles should connect these points. For example a uniform cubic B-spline surface with four control points in each row and five control points in each column is defined over parameter values [3,4]x[3,5]. If the u step size was 0.1 and the v-step size was 0.2, then you would evaluate the surface at parameter values:

(3.0,3.0)
(3.1,3.0)
...
(4.0,3.0)
(3.0,3.2)
(3.1,3.2)
...
...
(4.0,5.0)

and the triangles to output would be as follows, where Q(u,v) is the surface evaluated at (u,v). (Actually you can pick a different way to triangulate the points if you want.)

Q(3.0,3.0) Q(3.1,3.0) Q(3.1,3.2)
Q(3.0,3.0) Q(3.1,3.2) Q(3.0,3.2)
Q(3.1,3.0) Q(3.2,3.0) Q(3.2,3.2)
Q(3.1,3.0) Q(3.2,3.2) Q(3.1,3.2)
...

Viewer

A viewer with a crystal ball interface written in C++, using glut and openGL, is provided. It can read in files of triangles in the format described above. You might simply add code to it to do your assignment. It is documented.

Download Viewer (9k, tar-zip file)

Note you don't have to use this viewer, it is easy to write out your triangles to some other format, vrml for example and use a vrml browser to examine your results (other options like IV, OBJ, STL, etc.)

What you should hand-in

Please hand in

All of your source code
A brief description of how to compile and run your code