- Volume 8 Issue 4
An approach to compute characteristic curves such as section curves, reflection characteristic lines, and asymptotic curves on a surface is introduced. Each problem is formulated as a surface-plane inter-section problem. A single-valued function that represents the characteristics of a problem constructs a property surface on parametric space. Using a contouring algorithm, the property surface is intersected with a horizontal plane. The solution of the intersection yields a series of points which are mapped into object space to become characteristic curves. The approach proposed in this paper eliminates the use of traditional searching methods or non-linear differential equation solvers. Since the contouring algorithm has been known to be very robust and rapid, most of the problems are solved efficiently in realtime for the purpose of visualization. This approach can be extended to any geometric problem, if used with an appropriate formulation.
- Computer Aided Design v.12 no.2 Correction of Local Surface Irregularities Using Reflection Lines Klass,R. https://doi.org/10.1016/0010-4485(80)90447-9
- Computer Aided Design v.20 no.6 Smoothing Surfaces Using Reflection Lines for Families of Splines Kaufmann,E.;Klass,R. https://doi.org/10.1016/0010-4485(88)90112-1
- Computer Aided Geometric Design v.1 no.2 Detecting Surface Irregularities Using Isophotes Poeschl,T. https://doi.org/10.1016/0167-8396(84)90028-1
- Computer Aided Design v.26 no.4 Highlight-line Algorithm for Realtime Surface Quality Assessment Beier,K.;Chen,Y. https://doi.org/10.1016/0010-4485(94)90073-6
- Computer Aided Geometric Design v.5 no.4 Tracing Surface Intersections Bajaj,C.(et al.) https://doi.org/10.1016/0167-8396(88)90010-6
- Computer Aided Geometric Design v.7 no.1-4 A Marching Method for Parametric Surface Intersection Barnhill,R.;Kersey,S. https://doi.org/10.1016/0167-8396(90)90035-P
- 한국CAD/CAM학회 논문집 v.4 no.3 곡면간의 교차곡선 계산을 위한 개선된 Tracing 알고리즘 조두연(외)
- Austral. Comput. J. v.2 no.1 An Economical Method of Plotting Contours Palmer,J.
- ACM Trans. Math. Soft. v.10 TRICP: A Contour Plot Program for Triangular Meshes Preusser,A. https://doi.org/10.1145/2701.2772
- Mathematical Methods in Computer Graphics and Design Contouring Over Rectangular and Skewed Rectangular Grids - An Introduction Sutcliffe,D.;Brodlie,K.(Ed.)
- VIEWX - ISOX, Documentation of a Program System to Create Graphics Representations and Countour Plots of a Thress Dimensional Surface Beier,K.P.
- Ph.D. dissertation, University of Michigan Direct Manipulation of Curve and Surface Properties Using a Piecewise Polynomial Basic Function Lu,Y.
- KSME International Journal v.15 no.2 Efficient Algorithm for Real-time Generation of Reflection Lines Kang,J.(et al.)
- Curves and Surfaces for Computer Aided Geometric Design(4th Ed.) Farin,G.
- IEEE Computer Graphics and Applications v.12 no.5 Surface Interrogation Algorithms Hagen,H.(et al.) https://doi.org/10.1109/38.156013
- Computer Aided Geometric Design v.18 Are Isophotes and Reflection Lines the Same? Theisel,H. https://doi.org/10.1016/S0167-8396(01)00063-2
- Lectures on Classical Differential Geometry Struik,D.