## Images and Pictures of Recent Research Projects:

### Metamorphosis of freeform surfaces

This sequence of three images is a samples of a small animation created by a metamorphosis process of freeform NURBs surfaces.

### Matching of freeform curves

A matching algorithm is introduced to generate an improve metamorphosis of freeform curves. The left shows direct convex combination while the right shows the result of applying the matching algorithm. Note the back and tail of the oryx.

### Sculptured Surface Modeling

This model of the B58 plane was modelled using the IRIT modeling environment and raytraced using the rayshade ray tracer.

Another high quality scene that was modelled using the IRIT modeling environment and raytraced using the rayshade ray tracer. This scene as well as the B58 above were constructed using various freeform surface modeling tools such as ruled surface (wings of B58), surface of revolution (the table and dishes), sweep (the cushion and base of chairs), and skinning (the fuselage of the B58). Similar geometries such as the engines of the B58 or the chair were instantiated several times using rigid motion transformations.

### Depth Cueing based Rendering

Rendering with depth cueing for both rendered using rayshade images (left) and postscript figures (right). The postscript version also supports haloed lines. Both examples were created using tools that are part of the IRIT modeling environment.

### Line Art Rendering

Adaptive extraction of isoparametric curves is employed herein to create illustrative imagery exploiting diferent shaders. The image on the left enhances silhouette regions while the image on the right uses cosine shader.

### Ruled Tracing

Ruled tracing of adaptive isoparametric curves is a novel rendering technique to directly scan convert freeform parametric surfaces. Herein, special affects such as texture and bump mapping are intermixed with shadow computation. No polygnal approximation of the freeform surfaces is involved in this process. Joint work with Postech, Korea.

### Curvature Analysis of Freeform Surfaces

In this sequal, three images of the Utah Teapot are shown with color maps that represents the Gaussian (left), Mean (middle), and sum of squares of principle curvatures (sqrt(k1^2 + k2^2)). These curvature properties were computed as scalar fields using tools provided in the IRIT modeling environment, were represented in piecewise polynomial parametric form, and were rendered back on top of the Utah Teapot using the IRIT rendering tool that supports texture mapping of scalar fields. In all three images, Red denotes high values, Blue low values, and Green intermediate values.

### Point-Curve Bisector Surface

The bisector surface of a curve and a point is rational! These examples show the shape of the bisector surface for a parabolic arc and a point in the plane (left) and out of the plane (right). The left image shows that the point-curve bisector is a special case of the curve-curve bisector with a vertical line. Created using the IRIT modeling environment as a joint work with Postech, Korea.

### Curve-Curve Bisector Surface

The bisector surface of two rational space curves in general 3-space position is rational! These examples show the shape of the bisector surface for an ellipse and a line and for a round square and a line. Both surfaces were computed symbolically and are represented using rational forms. Created using the IRIT modeling environment as a joint work with Postech, Korea.

### Virtual Reality and the WWW

This project investigates the mean to map various data (text, images, movies, sound, etc.) onto virtual environments. The two images provided herein show examples of a simple virtual environment where the images displayed are the result of a query posted to the network. Created using the IRIT modeling environment, Performer from SGI and W3QS WWW query language.

### Line Art Rendering of Parametric and Implicit Forms

Line art illustrations are created in this project, using strokes that are developed out of point distributions on the freeforms. This scheme can be employed for both parametric and implicit forms. Here, the chess set and the light bulbs are two examples of parametric forms, whereas the tubes' joint is a result of an implicit iso surface defined over a trivariate polynomial function and the facial figure is an output of an iso surface extraction out of the MRBrain model from UNC. both last examples employs the principal curvatures as the direction of the strokes. Created using the IRIT modeling environment.