Work Gallery - Computer Aided Geometric Design (Surface Modeling)

Surface offsetting using 3D distance volumes [IJAMT 2005a]

This work presents a method for generating an offset B-spline surface that lies at a distance r from the given surface. It basically uses the 3D distance volume of a given surface. (a) Input surface of a human head model; (b) Triangular mesh of the input surface (c) Offset points in a slice of the 3D distance volume; (d) Serial offset cross-sections (e) Fitted B-spline curves made compatible; (f) Lofted B-spline offset surface

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B-spline surface representation of functional surfaces [IJAMT 2001]

This work presents an approximate lofting method for B-spline surface fitting to a functional surface within a specified accuracy. It adopts adaptive sampling and multiple B-spline curve fitting. The method is very effective when the surface shape is longish or the cross-sectional curves vary regularly in shape along a specific direction. The method is applied in designing an aspheric optical lens used as a part of a laser scanning unit(LSU). The left image has been generated with ray tracing techniques.

(a) Isoparametric curves sampled from the above lens functional surfaces and made compatible B-spline curves via multiple B-spline curve refitting (b) Control net of a B-spline surface generated by approximately lofting the B-spline curves (c) Wireframe of the B-spline surface; (d) Shaded image of the B-spline surface Lofting, also known as skinning, is a process of passing a smooth surface through a set of cross-sectional curves. When quite a number of curves are given, a surface interpolating all the compatible curves can be a bulky and redundant representation. In this case, it is more preferable to approximate the curves without sacrificing the accuracy. In view of NURBS surfaces, their control points need to be reduced as many as possible. This is called approximate lofting. Such data reduction speeds up most of downstream processes and leads to a decrease in storage requirements.

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Surface modeling with approximate curve compatibility [CAD 2000]

What is the approximate curve compatibility? (a) Input curves not compatible (b) Wireframe display of a B-spline surface generated by lofting the compatible B-spline curves (c) Shaded display of the B-spline surface (a) Input scan data (b) B-spline curves made compatible via multiple curve fitting (c) Control net of a B-spline surface generated via lofting the compatible B-spline curves (d) Wireframe of the B-spline surface