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## [Bar84]  Global and Local Deformations of Solid Primitives

 Barr:1984:GLD (Article) Author(s) Barr A. Title « Global and Local Deformations of Solid Primitives » Journal ACM SIGGRAPH Computer Graphics, Proceedings of ACM SIGGRAPH 84 (Minneapolis, MN, July 23--27, 1984) Volume 18 Number 3 Page(s) 21--30 Year 1984

 Abstract New hierarchical solid modeling operations are developed, which simulate twisting, bending, tapering, or similar transformations of geometric objects. The chief result is that the normal vector of an arbitrarily deformed smooth surface can be calculated directly from the surface normal vector of the undeformed surface and a transformation matrix. Deformations are easily combined in a hierarchical structure, creating complex objects from simpler ones. The position vectors and normal vectors in the simpler objects are used to calculate the position and normal vectors in the more complex forms; each level in the deformation hierarchy requires an additional matrix multiply for the normal vector calculation. Deformations are important and highly intuitive operations which ease the control and rendering of large families of three-dimensional geometric shapes.

 BibTeX code ``````@article{Barr:1984:GLD, number = {3}, volume = {18}, month = jul, author = {Alan H. Barr}, optkey = {}, optstatus = {url}, abstract = {New hierarchical solid modeling operations are developed, which simulate twisting, bending, tapering, or similar transformations of geometric objects. The chief result is that the normal vector of an arbitrarily deformed smooth surface can be calculated directly from the surface normal vector of the undeformed surface and a transformation matrix. Deformations are easily combined in a hierarchical structure, creating complex objects from simpler ones. The position vectors and normal vectors in the simpler objects are used to calculate the position and normal vectors in the more complex forms; each level in the deformation hierarchy requires an additional matrix multiply for the normal vector calculation. Deformations are important and highly intuitive operations which ease the control and rendering of large families of three-dimensional geometric shapes.}, title = {{G}lobal and {L}ocal {D}eformations of {S}olid {P}rimitives}, localfile = {papers/Barr.1984.GLD.pdf}, doi = {http://doi.acm.org/10.1145/964965.808573}, pages = {21--30}, journal = SIGGRAPH84, year = {1984}, organization = {ACM}, }``````

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