|
|
Teaching aids for 2D computer graphics
Malina, Jakub ; Průša, Zdeněk (referee) ; Rajmic, Pavel (advisor)
In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.
|
|
|
Pythagorean hodograph splines
Kadlec, Kryštof ; Šír, Zbyněk (advisor) ; Lávička, Miroslav (referee)
In this thesis the main object of our concern is a Pythagorean hodograph B- spline curve. We recall notions of both Pythagorean hodograph (PH) curves and B-spline functions separately first. Then we put these fields together to generalize PH curves to their B-spline instances. We encapsulate these curves in various spaces under one algebraic structure using the formalism of Clifford algebras. We consider both Euclidean and Minkowski spaces of lower dimensions which give room for real applications and use of these curves. We support our results by giving numerous examples. 1
|
|
|
Curves with pythagorean hodograph
Kadlec, Kryštof ; Šír, Zbyněk (advisor) ; Šmíd, Dalibor (referee)
In the thesis we will look at curves with pythagorean hodograph (PH curves) whose speed is polynomial with respect to parameter. We will consider planar PH curves of degree 3 (PH cubics) exclusively. We will present their complex representation and preimage. Preimage is a simpler curve from which a PH curve is created and which determines its properties. First we will look at the basic properties of PH curves with respect to their preimage. The main aim of the thesis is determining continuousness of joints of PH curves on the basis of the shape of their preimage. We will give specific conditions on preimage for achieving certain types of continousness. Finally we will give some examples in order to illustrate the results. 1
|
|
|
Teaching aids for 2D computer graphics
Malina, Jakub ; Průša, Zdeněk (referee) ; Rajmic, Pavel (advisor)
In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.
|
|
|
Teaching aids for 2D computer graphics
Malina, Jakub ; Průša, Zdeněk (referee) ; Rajmic, Pavel (advisor)
In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.
|
guest ::
