Surface Tessellation: Assignment #5

Overview

Provided Commands

fov angle
translate  tx ty tz
scale  sx sy sz
rotate  angle  ax ay az
lookat  fx fy fz  ax ay az  ux uy uz
push
pop

In addition to these standard transformation commands, you will also need a few additional commands:

clear

This already-provided command clears the screen.

light  x y z

This command specifies the location of the light source. It is actually provided in the sample code.

color r g b

Specifies the ambient and diffuse color of a surface. We will use a very simple lighting model for this project.

begin
vertex x y z
vertex x y z
...
end

The above commands describe a polygon. As usual, the current transformation matrix transforms the polygon vertices. You should look at the code that implements this command carefully because you will do something similar to create polygons that tessellate the sphere. Pay particular attention to the surface normals.

Commands You Will Write

sphere  x y z  radius

This command should cause your program to create a sphere at the given location and radius. You should NOT use the GLUT sphere command, but instead create your own sphere out of polygons. You can do this in any manner you wish-- latitude/longitude or subdivided icosahedrons are two possibilities.

roughness  first_offset  scale_factor  max_depth

This command specifies two parameters for the fractals that are specified following this command. The "first_offset" parameter specifies the upper bound on the range of height offsets for the y-axis vertical displacement of the first midpoints. If "first_offset" is zero, created fractals will just be flat triangles. The random values that you add in the vertical direction should be in the range of [-first_offset, +first_offset], that is, your random number ranges should be centered at zero. The "scale_factor" specifies a multiplying factor (which should be less than one) with which to multiply the current offset for the next midpoints in the recursive fractal creation. The "max_depth" parameter (an integer) specifies how many levels of triangle subdivision to perform. A "max_depth" value of zero will result in no triangle subdivision.

seed  int_value

This command allows you to specify an integer value that will be added to each of the random number seeds that you use to create your fractals. The default value of this seed should be zero, which means that your fractals will look exactly the same each time you run your program. By specifying a different seed, however, you can create fractals that take on a variety of different looks.

fractal  x1 y1 z1  x2 y2 z2  x3 y3 z3

This command specifies the (x,y,z) location for three vertices of a triangle that will be subdivided to create a fractal. Use the standard recursive midpoint subdivison that splits each triangle into four new triangles.

The last component of this assignment is for you to create some form of color variation for your fractal moutains. You are free to choose your own method for varying the color of the polygons. One common method is to use some function of the height to change the moutain colors, with white at the peaks and greens and browns lower down. Feel free to use some form of randomness to add variation to the colors if you wish. Note that when a fractal is drawn, the color given in the "color" command is ignored.

Your Own Scene

Provided Code and Suggestions

The example code is called "surfaces.c". Note that the provide makefile links this code to the CLI routines, but it does *not* link to the GLUT commands. You must create your sphere and fractal commands from the polygon drawing commands glBegin(GL_POLYGON), glVertex3f(x,y,z), and glEnd(). You will find that in order to properly light your spheres, you must specify the surface normals using the command glNormal3f() either before each vertex (for smoothly shaded sphere) or each set of vertices that make up a triangle for your fractals.

To draw a fractal, you should be able to write a straightforward recursive procedure that takes three vertex positions and the current "depth" of the recursion and decides whether to draw a triangle or to split the triangle into four smaller fractal triangles (the recursion). Try out the files "frac.cli" and "islands.cli".

The trickiest part of this assignment is to seed the random number generator correctly in order to prevent cracks in your fractal surface. You can use the routine "rand()" to give you random values that you should then scale to the appropriate range. The routine "srand(seed)" will allow you to seed the random number generator based on the position of the two vertices of the side on which you are determining the new midpoint. Use the (x,y,z) coordinates of the edge midpoint to come up with a unique, large integer with which to seed the random number generator. Call "srand()" with this seed value before using "rand()" to come up with the random height. Note that your fractal images will not look exactly the same as the example images because you will use a different seed function. The overall visual characteristics, however, should be the same.

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