Proceedings: GI 1996

A technique for constructing developable surfaces

Meng Sun, Eugene Fiume

Proceedings of Graphics Interface '96: Toronto, Ontario, Canada, 22 - 24 May 1996, 176-185

DOI 10.20380/GI1996.21

  • BibTeX

    @inproceedings{SunFiume-gi96,
     title = {A technique for constructing developable surfaces},
     author = {Meng Sun and Eugene Fiume},
     booktitle = {Proceedings of the Graphics Interface 1996 Conference, May 22-24, 1996, Toronto, Ontario, Canada},
     year = {1996},
     month = {May},
     isbn = {0-9695338-5-3},
     publisher = {Canadian Human-Computer Communications Society},
     url = {http://graphicsinterface.org/wp-content/uploads/gi1996-21.pdf},
     pages = {176--185}
    }
    

Abstract

Paper, sheet metal, and many other materials are approximately unstretchable. The surfaces obtained by bending these materials can be flattened onto a plane without stretching or tearing. More precisely, there exists a transformation that maps the surface onto the plane, after which the length of any curve drawn on the surface remains the same. Such surfaces, when sufficiently regular, are well known to mathematicians as developable surfaces. While developable surfaces have been widely used in engineering, design and manufacture, they have been less popular in computer graphics, despite the fact that their isometric properties make them ideal primitives for texture mapping, some kinds of surface modelling, and computer animation. Unfortunately, their constrained isometric behaviour cuts across common surface formulations. We formulate a new developable surface representation technique suitable for use in interactive computer graphics. The feasibility of our model is demonstrated by applying it to the modelling of a hanging scarf and ribbons and bows. Possible extensions and interesting areas of further research are discussed.