CSE 557: Computer Graphics

Spring Quarter 1999

Project 3: Subdivision Surfaces Date Assigned: 7 May 1999 Date Due: 20 May 1999 Artifact Due: 25 May 1999

Project Description

Getting Started

Required Functionality

• Support both non-interpolating (Loop) and interpolating (Butterfly) subdivision. Use the evaluation mask to calculate final vertex positions if necessary, and the tangent masks to calculate vertex normals.

• Add support for feature edges and vertices. Your subdivision editor should have an interface for selecting a vertex or an edge and then marking (or unmarking) it as a feature.

• Implement at least one bells worth of extensions from the list below. A whistle is worth one half bell.

Bells and Whistles

Implement Doo-Sabin or Catmull-Clark subdivision surfaces (or both.)

Add support for surfaces with boundaries. Intuitively, a point lies on the boundary if it has a surface neighborhood on one side, but not the other. In a triangle mesh, a boundary edge has a triangle on one side but not the other.

Add support for texture mapping. This requires defining (u,v) coordinates for the control vertices and applying the subdivision rules to the (u,v) coordinates as well as the vertex positions. See [DeRose 98] for details. Of course, you need to read in an image and show that you can map it over the surface.

Add support for semi-sharp features as in [DeRose 98] or [Sederberg et al 98]. This amounts to varying the subdivision masks across subdivision levels and spatially for a few iterations, and then pusing the vertices to the limit. Extra credit for a nice user interface.

Faster editing

Improve the speed of editing operations by only resubdividing the area of the surface that is affected when you move a control vertex (the region of influence of the control point being moved).

Improve the included "lo res" editing switch so that the surface displayed while editing is subdivided as far it can while still remaining responsive. Therefore, if you move a control point slowly you will see a higher resolution model than if you move a control point quickly. And if you stop moving the control point for long enough the display will update with a higher resolution version. (Remember that if you use an evaluation mask to send vertices to their limit positions you can't continue to subdivide!)

Combining these last two bells could would be worth three bells.

Editing the base mesh

Provide an interface for snapping vertices to a grid. It's common to want to create simple "canonical" models that have symmetry, e.g., cylinder-like and donut-like shapes. Snapping the control points to a grid helps ensure the desired regularity.

Allow the user to add more control points to the base mesh in places where they want more control. A simple implementation of this would let them choose an edge and split it. Better would be to let them click anywhere and add a vertex there.

Let the user change the genus of the base mesh. Then he or she can, for example, turn a cube into a donut. Just figuring out a good interface is a challenge. Perhaps selecting two faces and "joining" them?

User interface

Let the user select several control vertices and move them as a group.

Add a simple form of multiresolution edit. Here's the idea: when moving a control point, a neighborhood (adjustable in size) of control points around it also move. The amount that the neighboring points move depends on their distance from the selected control point. The distance metric could be based on number of edge steps from the control point to the neighbor, or it could be the Euclidean distance in 3-space, or even based on an approximation to the shortest distance measured over the surface (geodesic distance).

Implement direct manipulation of the surface, i.e. let the user grab any point on the surface and move it to where they want it. What should the rest of the surface do?

Level of detail (LOD)

Automatically adjust the amount of subdivision for the model using some measure of error, and a tolerance (or target mesh size). For your error measure you could fit a plane to a vertex neighborhood and compute the distance from the vertex to that plane. If any vertex exceeds the tolerance, subdivide up to the user-specified limit.

Implement a view-dependent error metric. For example, to keep the silhouettes accurate, you could compute the distance between a vertex and the nearest point on the planar fit as before, but do the distance calulation in projected screen space. Then, for a specified tolerance, you can use fewer polygons if the object is moved further from the camera. More credit is available if you take apparent errors in shading into account (see, e.g., Hoppe's SIGGRAPH '97 paper on view-dependent progressive meshes).

Implement adaptive subdivision. Either style of LOD can be enhanced by subdividing different areas of the model to different levels. With an object-based error metric, the higher curvature, more detailed areas of the object will require more subdivision. With a view-dependent error metric, silhouettes will be more highly subdivided.

Brief Hints

• The three mouse buttons rotate, translate, and zoom the scene. With shift and control they can be used to move control points, giving you a total of six (count them!) ways to edit a control point.

• Most of your work will start in average.hh and average.cpp which contain the code for the mediocre built-in subdivision schemes.

• The method that changes the subdivision scheme is void CControl::OnSelchangeSubstyle().