Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
The algorithmic beauty of plants
The algorithmic beauty of plants
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
A collision-based model of spiral phyllotaxis
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Convex surface fitting with parametric Be´zier surfaces
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Techniques for interactive design using the PDE method
ACM Transactions on Graphics (TOG)
Mathematical Models in Biology
Mathematical Models in Biology
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This paper presents a free-form model for surface deformation and growth. A general framework with bicubic patches is developed to generate a growing surface. The key component of this method is to enable the control points to move such that we achieve satisfactory results when the surface growth is constrained by an evolutionary formulation. The evolution theory must take account of natural and artificial pertubations in the growth cycle. This implies that the transient of the control points must be flexible and adaptable. A simple real-time collision detection method is developed to trace the surface growth correctly in an efficient manner. The application we are interested in involves the animation of the flower development. Therefore, the modeling must be accurate and suitable for all possible growth patterns. Petals are arranged according to sound biological principles, therefore, any growth must demonstrate collision detection and deformation constraints. We show that the model presented here upholds these principles.