CS418 Lab 11

CS 418: Laboratory 11

Implicit Surfaces

Introduction.

In this lab you will investigate implicit surface generation. Implicit surfaces are generated by finding "level surfaces" in a 3D field. That is, by placing polygons in all of the voxels which have scalar data of a certain value. The surface descriptions often take forms familar from analytical geometry. For instance, a unit sphere at the origin is described by

x^2 + y^2 + z^2 - 1.0

when a surface is fit to the points in 3D which have a value of zero.

Procedure

Download:

heart.net
heart.cfg
SurfaceCombine.net
SurfaceCombine.cfg
blobbyMacroUI.net
blobbyMacroUI.cfg
Put the following in ~yourID/.DXmacros so than when DX starts up it will find these macros. Note the programs in this exercise will not run without these macros.

The program heart.net takes as input an implicit function of x,y,z and forms an surface. The function is calculated at grid points, then polygonalized by isosurface rendering, assuming an isosurface value of zero. For example the formula

(2*x^2 + y^2 + z^2 -1)^3 - 0.2*x^2*z^3 - y^2*z^3

creates a heart-shaped object.

Different functions of x,y,z will produce different shapes. (Note that for different functions, you may have to modify the range limits of the space defined by the Construct module.) As an example, the following image was made by defining an implicit sphere in a separate module from the heart, then morphing between them by linearly intropolating between the two 3D fields. In this case, mixing .9 of the heart 3D field with 0.1 of the sphere 3D field. The sphere used was:

x^2 + y^2 +(z+.25)^2 -.5

The program SurfaceCombine.net shows how to combine two implicit surfaces to simulate the "union" operation as used in constructive solid geometry (see page 35 of Watt). Three new macros are used in this program; InitCSG, UnionCSG, and MakeCSGsurface. You can inspect (or modify) the macros using the "Open Selected Macro" option in the "Windows" menu of the visual program editor. The two cylinder surfaces are combined (in the UnionCSG macro) using a min(a,b) function so that the voxels which are in the interior of either cylinder are interior to the result. (Remember that an implicit function changes sign as the surface is crossed and that for the surfaces used here, that points inside have a negative value.) The image below is the result of the union of two cylinders.

The program blobby.net computes an implicit surface based on spherical fields of influence which can add together. See one of last year's student projects for more information on blobby functions. The spherical fields can have positive and negative field strengths. An example from blobby.net shows four positive spheres (transparent red) and two negative spheres (blue) which when summed together, then passed thorough an isosurface module produce the object shown to the right.

Assignment:

Execute the programs to understand their behavior, then modify them as follows:

Modify heart.net to generate a torus from an implicit function of (x,y,z). You will need to construct a function which is negative if the position (x,y,z) is within a certain distance of a circle and positive otherwise. Include interactors to set the radius of the torus and the radius of its cross-section. Optimize the torus generation by constructing a grid into which the torus just fits.
To get a feel for the number of polygons on this surface, add a SimplifySurface module between the isosurface module and following modules. Also add a Describe module ot the output of the SimplifySurface module. Change the the parameter in the SimplifySurface module which controls surface accuracy, while reading the object description in the Message window. The number of "data values" is also the number of vertices in the object. What is the minimum number of vertices you can use to get a reasonable approximation of a heart? You can use the Shade module with the "how" parameter set to "faceted" to see the individual polygons. Optimization of polygon count will be essential later in the semester when you deal with lots of objects.
Extend SurfaceCombine.net to perform the CSG operations of intersection and subtraction by writing two new macros called IntersectCSG and SubCSG. Provide interactors for choosing any combination of two spheres, cylinders, tori, or cones. Provide interactors for performing a union, intersection, or subtraction of the two selected shapes. That is, your program should be able to, for example, select a sphere and a cone, and form the subtraction of cone-minus-sphere or sphere-minus-cone or union the sphere and the cone or intersect the sphere and the cone. Shown below are the intersection of two cylinders and one cylinder "minus" the other.

The image below is formed as
((superquadric minus torus) union cylinder),
but with about 1% white noise added to the 3D field.
Use the interactors in blobby.net to make a human head with recognizable (but not necessarily artistic) eyes, nose, mouth and ears.

Some results from 1997.

Some results from 1998.

Be prepared to demo the programs to show the torus generator, the CSG operations, and the head you designed. The grader will exercise all interactors.

You should be able to explain your programs. You should use transmitters/receivers, macros, and comments in the "Notation" field of each module so that you and the grader can understand the program. Control panels, if any, should be well organized, labeled, and with the appropriate numeric ranges.

The Lab 11 grading guide will be filled out by a consultant during section to evaluate your work.