A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve lies inside the convex hull of the control points, and the segments of the broken line connecting the control points are tangent to the curve. To construct the...

A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. W...

Protopsaltis, Antonios, A.P. PhD, Computer Science Department, University of Ioannina, Greece. January, 2010. Reconstructing 3D CAD Models based on geometrically constrained cross sections Thesis Supervisor: Fudos, Ioannis. We introduce a novel approach to reconstructing 3D objects from cross sections of point clouds acquired by laser scanning. Cross sections are almost planar clusters of 3D po...

In modern commercial CAD and systems, a wide variety of part shapes for dies and molds are usually represented in parametric curves (or surfaces) like the Bezier curve, B-spline, and NURBS. However, conventional CNC machines only provide line or circular interpolators. In order to perform the machining of molds, the shapes and desired tool paths designed using CAD/CAM systems are typically appr...

Ghandmjit L. Bajaj t Department of Computer Science, Purdue University, West Lafayette, IN 47907 In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained by different characterizations of the zero contours of the Bernstein-Bezier (BB) form of bivariate po...

Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inf...

Particle size distribution (PSD) is a fundamental physical property of soils. Traditionally, the PSD curve was generated by hand from limited data of particle size analysis, which is subjective and may lead to significant uncertainty in the freehand PSD curve and graphically estimated cumulative particle percentages. To overcome these problems, a log-cubic method was proposed for the generation...

Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortio...

Since the mode of Pythagorean-Hodograph curve’s derivate is a polynomial, its involute should be a rational polynomial. We study the expression form of PH cubic’s involute, discovering that its control points and weights are all constructed by corresponding PH cubic’s geometry property. Moreover, we prove that cubic PH curves have neither cusp nor inflection; there are two points coincidence in...