TY - GEN
T1 - Geometric modeling with conical meshes and developable surfaces
AU - Liu, Yang
AU - Pottmann, Helmut
AU - Wallner, Johannes
AU - Yang, Yongliang
AU - Wang, Wenping
PY - 2006
Y1 - 2006
N2 - In architectural freeform design, the relation between shape and fabrication poses new challenges and requires more sophistication from the underlying geometry. The new concept of conical meshes satisfies central requirements for this application: They are quadrilateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass structures. Moreover, they possess a natural offsetting operation and provide a support structure orthogonal to the mesh. Being a discrete analogue of the network of principal curvature lines, they represent fundamental shape characteristics. We show how to optimize a quad mesh such that its faces become planar, or the mesh becomes even conical. Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant way of modeling developable surfaces.
AB - In architectural freeform design, the relation between shape and fabrication poses new challenges and requires more sophistication from the underlying geometry. The new concept of conical meshes satisfies central requirements for this application: They are quadrilateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass structures. Moreover, they possess a natural offsetting operation and provide a support structure orthogonal to the mesh. Being a discrete analogue of the network of principal curvature lines, they represent fundamental shape characteristics. We show how to optimize a quad mesh such that its faces become planar, or the mesh becomes even conical. Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant way of modeling developable surfaces.
KW - developable subdivision surface
KW - developable surface
KW - discrete differential geometry
KW - nonlinear subdivision
KW - offset mesh
KW - principal mesh
KW - quad mesh
KW - surfaces in architecture
UR - http://www.scopus.com/inward/record.url?scp=77954004435&partnerID=8YFLogxK
U2 - 10.1145/1179352.1141941
DO - 10.1145/1179352.1141941
M3 - Conference contribution
AN - SCOPUS:77954004435
SN - 1595933646
SN - 9781595933645
T3 - ACM SIGGRAPH 2006 Papers, SIGGRAPH '06
SP - 681
EP - 689
BT - ACM SIGGRAPH 2006 Papers, SIGGRAPH '06
T2 - ACM SIGGRAPH 2006 Papers, SIGGRAPH '06
Y2 - 30 July 2006 through 3 August 2006
ER -