Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving...Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and 3D.In this paper,B´ezier curves play an important role in the design of the letters.Three examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.展开更多
This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves.Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above.Bezie...This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves.Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above.Bezier curves find real life applications in diverse areas of Engineering and Computer Science,such as computer graphics,robotics,animations,virtual reality,among others.Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations,proof of related theorems,first and second order calculus related computations,among others.A Practical case is demonstrated using a graphical design,physical hand sketching,and programmatic implementation of two opposite-faced handless cups,all evolved using quadratic Bezier curves.The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript.This work will no doubt find relevance in computational researches in the areas of graphics,web programming,automated theorem proofs,robotic motions,among others.展开更多
The shadow of a circle casting on a unparallel plane is an ellipse, the shadow algorithm involves a perspective affine transformation. Under commonly used light, the transformation matrix for parallel circles of diffe...The shadow of a circle casting on a unparallel plane is an ellipse, the shadow algorithm involves a perspective affine transformation. Under commonly used light, the transformation matrix for parallel circles of different diameters casting shadows onto the same plane is identical. Using AutoCAD to get the shadow of a general object of revolution, it only needs to take a series of circles along the axis of symmetry and get their corresponding shadows of ellipses, drawing an envelope to cover all these silhouettes results in the required overall shadow. Then the discrete points of shadow contour line are projected back onto the original object surface, shadow on the object is obtained altogether.展开更多
With the improving of people＇s artistic aesthetic level, the art of pen drawing in all walks of life has been spread and ap- plied widely. However, the artistic effect of pen drawing is still far from perfect in the ...With the improving of people＇s artistic aesthetic level, the art of pen drawing in all walks of life has been spread and ap- plied widely. However, the artistic effect of pen drawing is still far from perfect in the current methods for generating image-based pen drawing automatically by using computer technology. Therefore, the new method for generating pen drawing with NURBS Curve defines the characteristics of pen drawing in detail and redesigns the algorithm flow chart of pen drawing. It solves the prob- lem of the description of details of pen drawing and improves curve effect of pen drawing with NURBS Curve. It＇s able to better ex- press the artistic conception of pen drawing and solve the problem of simulating pen drawing of any image by using computer art simulation technology.展开更多
Modeling the 3D geometric configuration of yarn is the base of building the 3D fabric structure. The surfaces of the yarns are modeled by many facets. To improve the efficiency of modeling, 3D yarn is usually designed...Modeling the 3D geometric configuration of yarn is the base of building the 3D fabric structure. The surfaces of the yarns are modeled by many facets. To improve the efficiency of modeling, 3D yarn is usually designed by Bezier curve, spline curve or B-spline curve on the principle of Computer Graphics. The paper reviews different 3D modeling methods for single yarn from the view of cross-section and central line. Some improvements for a better visual effect such as inserting twist and hairiness are illustrated as well. Based on the single yarn, the folded yarn and some fancy yarns can also be modeled in 3D space as long as the cross-sections of the control sections of the component single yarn are determined. Applications of the various 3D yarns are demonstrated. The advantages and the drawbacks of various methods are explained and compared as well. Comparatively speaking, modeling technology based on spline curve is more convenient and flexible, perhaps it is the most popular tool since it is capable of designing different kinds of yarns mentioned above and gets the maximum support from the different developing platforms such as OpenGL, 3DS-MAX, Solid Works CAD, etc.展开更多
基金the financial support of the Ministry of Science and Technology(MOST),Taiwan,under the recruitment of visiting science and technology personnel with subsidies 110-2811-E-002-518the support of sabbatical leave provided by the University of Southern Mississippi.
文摘Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and 3D.In this paper,B´ezier curves play an important role in the design of the letters.Three examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.
文摘This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves.Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above.Bezier curves find real life applications in diverse areas of Engineering and Computer Science,such as computer graphics,robotics,animations,virtual reality,among others.Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations,proof of related theorems,first and second order calculus related computations,among others.A Practical case is demonstrated using a graphical design,physical hand sketching,and programmatic implementation of two opposite-faced handless cups,all evolved using quadratic Bezier curves.The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript.This work will no doubt find relevance in computational researches in the areas of graphics,web programming,automated theorem proofs,robotic motions,among others.
文摘The shadow of a circle casting on a unparallel plane is an ellipse, the shadow algorithm involves a perspective affine transformation. Under commonly used light, the transformation matrix for parallel circles of different diameters casting shadows onto the same plane is identical. Using AutoCAD to get the shadow of a general object of revolution, it only needs to take a series of circles along the axis of symmetry and get their corresponding shadows of ellipses, drawing an envelope to cover all these silhouettes results in the required overall shadow. Then the discrete points of shadow contour line are projected back onto the original object surface, shadow on the object is obtained altogether.
文摘With the improving of people＇s artistic aesthetic level, the art of pen drawing in all walks of life has been spread and ap- plied widely. However, the artistic effect of pen drawing is still far from perfect in the current methods for generating image-based pen drawing automatically by using computer technology. Therefore, the new method for generating pen drawing with NURBS Curve defines the characteristics of pen drawing in detail and redesigns the algorithm flow chart of pen drawing. It solves the prob- lem of the description of details of pen drawing and improves curve effect of pen drawing with NURBS Curve. It＇s able to better ex- press the artistic conception of pen drawing and solve the problem of simulating pen drawing of any image by using computer art simulation technology.
文摘Modeling the 3D geometric configuration of yarn is the base of building the 3D fabric structure. The surfaces of the yarns are modeled by many facets. To improve the efficiency of modeling, 3D yarn is usually designed by Bezier curve, spline curve or B-spline curve on the principle of Computer Graphics. The paper reviews different 3D modeling methods for single yarn from the view of cross-section and central line. Some improvements for a better visual effect such as inserting twist and hairiness are illustrated as well. Based on the single yarn, the folded yarn and some fancy yarns can also be modeled in 3D space as long as the cross-sections of the control sections of the component single yarn are determined. Applications of the various 3D yarns are demonstrated. The advantages and the drawbacks of various methods are explained and compared as well. Comparatively speaking, modeling technology based on spline curve is more convenient and flexible, perhaps it is the most popular tool since it is capable of designing different kinds of yarns mentioned above and gets the maximum support from the different developing platforms such as OpenGL, 3DS-MAX, Solid Works CAD, etc.
