Planning a Purely Translational Motion for a Convex Object in Two Dimensional Sp
Planning a Purely Translational Motion for a Convex Object in Two Dimensional Sp
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In our eReader you can find the full English version of the book. Read Planning a Purely Translational Motion for a Convex Object in Two Dimensional Sp Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Planning a Purely Translational Motion for a Convex Object in Two Dimensional Sp
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The final step merges VorgiL) and VorsiR) to obtain the 5-Voronoi diagram of 5(1^). Note that the objects in S{W) which intersect both Qi and Q/j are split by the vertical line separating (2/, and g^ into two parts, one in L and the other in R. The present merge first calculates the 5-diagram for L U R (i. E. With each such object remaining split), and only then patches up -24- the diagram to obtain VorB(S(W)).
To merge the diagrams VorB{L), VorgiR), we have to cx)mpute the locus C of points wh...ich are equally fi-closest to an object in L and to an object in R. Following Kirkpatrick [Ki] we call C the contour separating L from R. It is easy to see that C is a simple, topologically closed curve since each vertex of the combined diagram has degree 3 (for details concerning this standard argument see e. G [LS]). Hence C partitions the plane into disjoint open connected regions each of which consists either entirely of points which are 5-closer to objects in L than to objects in R (in which case we call such a region, as in [LS], an L-region) or entirely of points which are 5-closer to objects in R than to objects in L (in which case we call such a region an R- region).
What to read after Planning a Purely Translational Motion for a Convex Object in Two Dimensional Sp?
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To quickly assess the difficulty of the text, read a short excerpt:
The final step merges VorgiL) and VorsiR) to obtain the 5-Voronoi diagram of 5(1^). Note that the objects in S{W) which intersect both Qi and Q/j are split by the vertical line separating (2/, and g^ into two parts, one in L and the other in R. The present merge first calculates the 5-diagram for L U R (i. E. With each such object remaining split), and only then patches up -24- the diagram to obtain VorB(S(W)).
To merge the diagrams VorB{L), VorgiR), we have to cx)mpute the locus C of points wh...ich are equally fi-closest to an object in L and to an object in R. Following Kirkpatrick [Ki] we call C the contour separating L from R. It is easy to see that C is a simple, topologically closed curve since each vertex of the combined diagram has degree 3 (for details concerning this standard argument see e. G [LS]). Hence C partitions the plane into disjoint open connected regions each of which consists either entirely of points which are 5-closer to objects in L than to objects in R (in which case we call such a region, as in [LS], an L-region) or entirely of points which are 5-closer to objects in R than to objects in L (in which case we call such a region an R- region).
What to read after Planning a Purely Translational Motion for a Convex Object in Two Dimensional Sp?
You can find similar books in the "Read Also" column, or choose other free books by D Leven to read onlineMoreLess
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