Implicit Surfaces Seminar, Spring 2012

... are needed to guide the moving direction from the original guess. These values can be computed by traversing the tree, which is one of the pros of Blob-Tree model. The ray tracing method is based on Lipschitz techniques to determine the roots. The efficiency of their ray tracer is further improved b ...

... are needed to guide the moving direction from the original guess. These values can be computed by traversing the tree, which is one of the pros of Blob-Tree model. The ray tracing method is based on Lipschitz techniques to determine the roots. The efficiency of their ray tracer is further improved b ...

1 Real-Time Algebraic Surface Visualization

... the equation f (x, y, z) = c, where x, y, z, c ∈ R. By reordering the terms, we can, without loss of generality, just consider the zero-set of the function, e.g. f (x, y, z) − c = 0. For this work, all functions and surfaces are considered to be real-valued. If the function f is an algebraic polynom ...

... the equation f (x, y, z) = c, where x, y, z, c ∈ R. By reordering the terms, we can, without loss of generality, just consider the zero-set of the function, e.g. f (x, y, z) − c = 0. For this work, all functions and surfaces are considered to be real-valued. If the function f is an algebraic polynom ...

Reverse Engineering Using a Subdivision Surface Scheme

... simple topological types such as deformed planar regions, cylinders, and tori. Therefore, it is impossible to use a single non-degenerate B-spline to model general closed surfaces or surfaces with handles. Multiple B-spline patches are needed for arbitrary topological surfaces; however, there are so ...

... simple topological types such as deformed planar regions, cylinders, and tori. Therefore, it is impossible to use a single non-degenerate B-spline to model general closed surfaces or surfaces with handles. Multiple B-spline patches are needed for arbitrary topological surfaces; however, there are so ...

Diffusion Curves: A Vector Representation for - maverick

... What makes creating this artwork so difficult using vector primitives is that most existing vector formats support only linear or radial gradients2 . Currently, the most sophisticated vector-based tool for handling complex gradients is the gradient mesh. A gradient mesh is a lattice with colors at ...

... What makes creating this artwork so difficult using vector primitives is that most existing vector formats support only linear or radial gradients2 . Currently, the most sophisticated vector-based tool for handling complex gradients is the gradient mesh. A gradient mesh is a lattice with colors at ...

unit ii – three dimensional concepts

... The viewing parameter of a 3D objects are i. Boundary representation ii. Space-partitioning representation 4. Define the term complementary colors. (UNIV QUES NOV/DEC 2007) Two different-color light sources with suitably chosen intensities can be produce a range of other colors. If the two color sou ...

... The viewing parameter of a 3D objects are i. Boundary representation ii. Space-partitioning representation 4. Define the term complementary colors. (UNIV QUES NOV/DEC 2007) Two different-color light sources with suitably chosen intensities can be produce a range of other colors. If the two color sou ...

An Efficient Filling Algorithm for Non

... scan conversion algorithms require a computationally expensive presorting and marking phase before they can compute the actual intervals of points contained in the region. The latter phase – specially for curved boundaries – requires careful attention to both geometric and numeric detail in order to ...

... scan conversion algorithms require a computationally expensive presorting and marking phase before they can compute the actual intervals of points contained in the region. The latter phase – specially for curved boundaries – requires careful attention to both geometric and numeric detail in order to ...

AP Calculus AB 2014

... Students will be expected to work in collaborative small groups. Each student will be teacher; each will be learner as they help each other master the material. Emphasis will be placed on student’s communicating their mathematical thinking within their groups, to the class as a whole, and on assessm ...

... Students will be expected to work in collaborative small groups. Each student will be teacher; each will be learner as they help each other master the material. Emphasis will be placed on student’s communicating their mathematical thinking within their groups, to the class as a whole, and on assessm ...

PPT - UBC Computer Science - University of British Columbia

... • tangent to curve at first control point is along line joining first and second control points • tangent at last control point is along line joining second last and last control points • curve lies entirely within convex hull of its control points – Bernstein polynomials (the basis functions) sum t ...

... • tangent to curve at first control point is along line joining first and second control points • tangent at last control point is along line joining second last and last control points • curve lies entirely within convex hull of its control points – Bernstein polynomials (the basis functions) sum t ...

State-Space Representations. Linearization

... To go from tf to ss: [A,B,C,D]=tf2ss(num,den) To go from ss to tf: [num,den]=ss2tf(A,B,C,D) New method: Create a tf object: >>tf_sys=tf(num,den) Convert to ss: >>sys_ss=ss(tf_sys) Extract system matrices: [A,B,C,D]=ssdata(sys_ss) Go back to tf: tf_sys=tf(sys_ss) Note: The ss realization in the old m ...

... To go from tf to ss: [A,B,C,D]=tf2ss(num,den) To go from ss to tf: [num,den]=ss2tf(A,B,C,D) New method: Create a tf object: >>tf_sys=tf(num,den) Convert to ss: >>sys_ss=ss(tf_sys) Extract system matrices: [A,B,C,D]=ssdata(sys_ss) Go back to tf: tf_sys=tf(sys_ss) Note: The ss realization in the old m ...

Lecture24

... Cubic splines the simplest representation with the appearance of smoothness and without the problems of higher order polynomials. ...

... Cubic splines the simplest representation with the appearance of smoothness and without the problems of higher order polynomials. ...

t - cs.csustan.edu - California State University Stanislaus

... • Algebraically, the point is defined by its coordinates (x,y) or (x,y,z) • We will usually see points as vertices in a geometric object • However, a triple (x,y,z) or a quadruple (x,y,z,w) will sometimes have another meaning, such as a color ...

... • Algebraically, the point is defined by its coordinates (x,y) or (x,y,z) • We will usually see points as vertices in a geometric object • However, a triple (x,y,z) or a quadruple (x,y,z,w) will sometimes have another meaning, such as a color ...

INTRODUCTION TO CAD

... – Stress (deflection analysis,I.e. numerical methods,FEM – Simulation of actual use – Optimizations – Applications – CAD/CAM integration – Process planning ...

... – Stress (deflection analysis,I.e. numerical methods,FEM – Simulation of actual use – Optimizations – Applications – CAD/CAM integration – Process planning ...

Approximate Algebraic Methods for Curves and Surfaces and

... interest in connection with so–called level–set techniques [Osher and Fedkiw 2003], where the function is given only at a 3D grid. Both representations are ambiguous. Parametric representations can be modified via parameter transformations, and the scalar fields defining implicitly defined curves or ...

... interest in connection with so–called level–set techniques [Osher and Fedkiw 2003], where the function is given only at a 3D grid. Both representations are ambiguous. Parametric representations can be modified via parameter transformations, and the scalar fields defining implicitly defined curves or ...

CS 536 Computer Graphics Bezier Curve Drawing Algorithms

... David Breen, William Regli and Maxim Peysakhov Department of Computer Science Drexel University ...

... David Breen, William Regli and Maxim Peysakhov Department of Computer Science Drexel University ...

ppt - Computing

... Consider the case of n+1 control points denoted as pk=(xk, yk, zk) where k varies from 0 to n The coordinate positions are blended to produce the position vector P(u) which describes the path of the Bézier polynomial function between p0 and pn n ...

... Consider the case of n+1 control points denoted as pk=(xk, yk, zk) where k varies from 0 to n The coordinate positions are blended to produce the position vector P(u) which describes the path of the Bézier polynomial function between p0 and pn n ...

(1-u)+u - inst.eecs.berkeley.edu

... In HW 1, HW 2, draw, shade objects But how to define geometry of objects? How to define, edit shape of teapot? We discuss modeling with spline curves Demo of HW 3 solution ...

... In HW 1, HW 2, draw, shade objects But how to define geometry of objects? How to define, edit shape of teapot? We discuss modeling with spline curves Demo of HW 3 solution ...

# Non-uniform rational B-spline

Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces. It offers great flexibility and precision for handling both analytic (surfaces defined by common mathematical formulae) and modeled shapes. NURBS are commonly used in computer-aided design (CAD), manufacturing (CAM), and engineering (CAE) and are part of numerous industry wide standards, such as IGES, STEP, ACIS, and PHIGS. NURBS tools are also found in various 3D modelling and animation software packages.They can be efficiently handled by the computer programs and yet allow for easy human interaction. NURBS surfaces are functions of two parameters mapping to a surface in three-dimensional space. The shape of the surface is determined by control points. NURBS surfaces can represent, in a compact form, simple geometrical shapes. T-splines and subdivision surfaces are more suitable for complex organic shapes because they reduce the number of control points twofold in comparison with the NURBS surfaces.In general, editing NURBS curves and surfaces is highly intuitive and predictable. Control points are always either connected directly to the curve/surface, or act as if they were connected by a rubber band. Depending on the type of user interface, editing can be realized via an element’s control points, which are most obvious and common for Bézier curves, or via higher level tools such as spline modeling or hierarchical editing.