Download presentation

Presentation is loading. Please wait.

Published byKian Boye Modified over 2 years ago

1
i MAGIS is a joint project of CNRS - INPG - INRIA - UJF iMAGIS-GRAVIR / IMAG A simple kinetic visibility polygon EWCG’02 Samuel Hornus, Claude Puech

2
iMAGIS-GRAVIR / IMAG Hypothesis : simply-polygonal obstacles known algebraic motion (everything can move) Goals : maintaining the visibility polygon continuously Solution : Kinetic Data Structure framework

3
iMAGIS-GRAVIR / IMAG Overview Kinetic Data Structures (KDS) Visibility polygon Detecting crossing events Updating the visibility polygon Conclusion contributions

4
iMAGIS-GRAVIR / IMAG Overview Kinetic Data Structures (KDS) Visibility polygon Detecting crossing events Updating the visibility polygon Conclusion

5
iMAGIS-GRAVIR / IMAG Kinetic Data Structures Moving Items (points, segments, …) Attributes on the items (convex hull, voronoï diagram) given with a proof of correctness for the static case Idea : animating the proof through time when items are moving certificate failure [Bash and Guibas 95]

6
iMAGIS-GRAVIR / IMAG Kinetic Data Structures Proof of correctness Certificate failure Proof updateAttribute update [Bash and Guibas 95]

7
iMAGIS-GRAVIR / IMAG Overview Kinetic Data Structures (KDS) Visibility polygon Detecting crossing events Updating the visibility polygon Conclusion

8
iMAGIS-GRAVIR / IMAG Visibility polygon n vertices / edges Cyclically ordered set of the n tangent rays The visible edge is stored between each pair of tangent rays

9
iMAGIS-GRAVIR / IMAG Overview Kinetic Data Structures (KDS) Visibility polygon Detecting crossing events Updating the visibility polygon Conclusion

10
iMAGIS-GRAVIR / IMAG Detecting Events consecutive rays in the ordered set

11
iMAGIS-GRAVIR / IMAG Detecting Events crossing event !

12
iMAGIS-GRAVIR / IMAG Detecting Events next crossing event

13
iMAGIS-GRAVIR / IMAG Detecting Events

14
iMAGIS-GRAVIR / IMAG Overview Kinetic Data Structures (KDS) Visibility polygon Detecting crossing events Updating the visibility polygon Conclusion

15
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon Knowing only the visibility polygon is not enough to maintain it, we need more data… We will use a weak radial decomposition of the scene.

16
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon Each tangent ray consists of - the vertex of « tangency »

17
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon Each tangent ray consists of - the vertex of « tangency » - the hit edge along the ray, beyond the vertex of tangency 8 8 8 8 8 8 8 8

18
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon Each tangent ray consists of -the vertex of « tangency » - the hit edge along the ray -the visible edge at its left 8 8 8 8 8 8 8 8 8

19
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon Each tangent ray consists of -the vertex of « tangency » - the hit edge along the ray -the visible edge at its left -the type of the tangency vertex see next slide… 8 8 8 8 8 8 8 8 8

20
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon Tangent ray type

21
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon R L hit2 hit1 Before the crossing

22
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon There is no other tangent ray between these ones Before the crossing R L hit2 hit1

23
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon C R L hit2 hit1 There is no other tangent ray between these ones Before the crossing C exists if and only if hit1 is different from hit2

24
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon R L hit2 hit1 Before the crossing, when C does not exist visible = hit2 = hit1

25
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon After the crossing, R L hit1 := R hit2 R L hit1 Before the crossing, when C does not exist visible = hit2 = hit1 visible := L

26
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon R L hit2 Before the crossing, when C does not exist visible = C C hit1 = C

27
iMAGIS-GRAVIR / IMAG Updating the Visibility Polygon After the crossing, L C R hit1 hit2 R L Before the crossing, when C exists visible = C C visible := L hit1 = C

28
iMAGIS-GRAVIR / IMAG Conclusion Pros Concave (simple) polygons Constant time processing of an event Cons High quantity of crossing events Future Work What about 3d ?

29
iMAGIS-GRAVIR / IMAG A simple kinetic visibility polygon Thank you for your attention Any questions ?

Similar presentations

OK

A brief and sketchy intro to 3D Convex Hulls Rodrigo Silveira GEOC 2010/11 - Q2.

A brief and sketchy intro to 3D Convex Hulls Rodrigo Silveira GEOC 2010/11 - Q2.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 500 mw turbo generators Ppt on effective communication skills Ce ms ppt online Ppt on resistance temperature detector formula Ppt on communication skills training Perspective view ppt on ipad Download ppt on mind controlled robotic arms manufacturers Ppt on mobile number portability in india Ppt on tsunami and earthquake Free ppt on festivals of india