Abstract
To overcome the topological constraints of non-uniform rational B-splines, T-splines have been proposed to define the freeform surfaces. The introduction of T-junctions and extraordinary points makes it possible to represent arbitrarily shaped models by a single T-spline surface. Whereas, the complexity and flexibility of topology structure bring difficulty in programming, which have caused a great obstacle for the development and application of T-spline technologies. So far, research literatures concerning T-spline data structures compatible with extraordinary points are very scarce. In this paper, an efficient data structure for calculation of unstructured T-spline surfaces is developed, by which any complex T-spline surface models can be easily and efficiently computed. Several unstructured T-spline surface models are calculated and visualized in our prototype system to verify the validity of the proposed method.
Highlights
With a series of excellent mathematical and algorithmic properties, non-uniform rational B-splines (NURBS) has been widely used in the field of computer aided geometric design for representing curves and surfaces
As the unstructured T-spline with an extraordinary point P4 shown in Fig. 8, assume that the orange arrow starting from P5 is the u direction of the local blending coordinate system of P5 and the red arrow represents the u direction of the face coordinate system denoted by yellow region
All the models are built from unstructured T-splines which include the extraordinary points except for the gearbox
Summary
With a series of excellent mathematical and algorithmic properties, non-uniform rational B-splines (NURBS) has been widely used in the field of computer aided geometric design for representing curves and surfaces. What calls for special attention is that in the unstructured T-mesh, a HE doesn’t have a specific direction and a vertex doesn’t have a corresponding global parameter coordinate This is the main difference between the proposed data structure and those constructed in a global coordinate system. As the unstructured T-spline with an extraordinary point P4 shown, assume that the orange arrow starting from P5 is the u direction of the local blending coordinate system of P5 and the red arrow represents the u direction of the face coordinate system denoted by yellow region. Bþc a þ bþcfdþeþ f bþc a þ bþc dþe d þ eþ f þ a a þb þ c dþe dþe þ f a a þbþcedþe þ f
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