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Application for 2D Curves Demonstration
Opletal, Pavel ; Švub, Miroslav (referee) ; Venera, Jiří (advisor)
This Bachelor's Thesis deals with planar curves used in computer graphics. It sums up general ideas of these curves and deals with particular methods for computing planar curves. It describes methods used for computing Ferguson cubic curves, Kochanek-Bartels spline, Cardinal spline, Catmull-Rom spline, Bézier curves and their modifications, Coons cubic curves, Coons cubic B-spline curves and NURBS. Practical part of this project deals with concept and impementation of tutorial, which demonstrates chosen curves.
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Mathematical description of vehicle motion trajectory
Lorenczyk, Jiří ; Popela, Pavel (referee) ; Porteš, Petr (advisor)
The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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Mathematical description of vehicle motion trajectory
Lorenczyk, Jiří ; Popela, Pavel (referee) ; Porteš, Petr (advisor)
The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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Application for 2D Curves Demonstration
Opletal, Pavel ; Švub, Miroslav (referee) ; Venera, Jiří (advisor)
This Bachelor's Thesis deals with planar curves used in computer graphics. It sums up general ideas of these curves and deals with particular methods for computing planar curves. It describes methods used for computing Ferguson cubic curves, Kochanek-Bartels spline, Cardinal spline, Catmull-Rom spline, Bézier curves and their modifications, Coons cubic curves, Coons cubic B-spline curves and NURBS. Practical part of this project deals with concept and impementation of tutorial, which demonstrates chosen curves.
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