C1-Continuous Coons-type Blending of Triangular Patches
نویسندگان
چکیده
A Gordon–Coons-type surface construction starts from three differentiable triangular surface patches, which are defined on the same triangular parameter domain. If one boundary curve of each fits a curvilinear triangle, then the defined surface interpolates to these curves. The connection between the resulting surface and the constituents is C1 continuous along the common boundary curves with the exception of the corner points. This surface definition is an extension of the Gordon–Coons definiton of a triangular surface patch constructed from three boundary curves.
منابع مشابه
ILDIKÓ SZABÓ C 1 - Continuous Coons - type Blending of Triangular Patches
A Gordon–Coons-type surface construction starts from three differentiable triangular surface patches, which are defined on the same triangular parameter domain. If one boundary curve of each fits a curvilinear triangle, then the defined surface interpolates to these curves. The connection between the resulting surface and the constituents is C1 continuous along the common boundary curves with t...
متن کاملElectronic Skeletons: Modeling Skeletal Structures with Piecewise Algebraic Surfaces
We present two algorithms to construct C1-smooth models of skeletal structures from CT/NMR voxel data. The boundary of the reconstructed models consist of a C1-continuous mesh of triangular algebraic surface patches. One algorithm first constructs Cl-continuous piecewise conic contours on each of the CT/NMR data slices and then uses piecewise triangular algebraic surface patches. to C1 interpol...
متن کاملAlgebraic grid generation on trimmed parametric surface using non-self-overlapping planar Coons patch
Using a Coons patch mapping to generate a structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic PDE methods when only C1 continuous boundary is given; the error of converting generic parametric C1 boundary curves into a specified representation form is also avoided. However, overlap may happen on some portions of the algebraically generated grid whe...
متن کاملConstruction and smoothing of triangular Coons patches with geodesic boundary curves
Given three regular space curves r1(t), r2(t) r3(t), t ∈ [ 0, 1 ] that define a curvilinear triangle, we consider the problem of constructing a C triangular surface patch R(u1, u2, u3) bounded by these three curves, such that they are geodesics of the constructed surface. Results from a prior study [6] concerned with tensor–product patches are adapted to identify constraints on the given curves...
متن کاملDiscrete Coons patches
We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a blend of variational principles. We show that no single blend of variational principles can produce...
متن کامل