Silhouette of a facetted polyhedra

[Dickinson, John]

Unfortunately, hardware solutions aren't practical in this case.  I do,
however, have the luxury of doing the projection calculations off-line.
 
John

-----Original Message-----
From: Hans Pedersen [mailto:Hans at paraform.com]
Sent: Tuesday, April 10, 2001 5:47 PM
To: 'Dickinson, John'
Subject: RE: Silhouette of a facetted polyhedra



Hi John, 

You can use graphics hardware to reduce this to a 2d image processing 
operation that will give you an approximation to centroid/area: 

Render all the polygons on the plane that you want and compute centroid/ 
area from the resulting binary image. You can get any accuracy you want 
by increasing the resolution of the image. 

Just an idea - good luck! 

Hans 

--- 
Hans K. Pedersen 
Sr. Software Engineer 
Paraform Inc 
Santa Clara, California, USA 

-----Original Message----- 
From: Dickinson, John [ mailto:John.Dickinson at nrc.ca
<mailto:John.Dickinson at nrc.ca> ] 
Sent: Monday, April 09, 2001 6:27 AM 
To: 'compgeom-discuss at research.bell-labs.com' 
Subject: Silhouette of a facetted polyhedra 


I want to get the shadow or projection of a 3D facetted polyhedra on a 
plane.  In other words I want to project all the triangles that describe the

surface of the polyhedra onto a plane and union them so that I have a 
polygon possibly with inclusions or holes (e.g. project a donut onto a plane

perpendicular to the axis of its hole). 

Can anyone point me to some code or papers that would give decent algorithms

for doing this (specifically the union of all the facets into a polygon)? 

The goal of this is to determine the centroid and area of the resultant 
projection.  Is there a way to do this without building the projected 
polygon first? 

John 

-- 
-((Insert standard disclaimer here))-|--- Washington Irving (1783-1859) ----

John Kenneth Dickinson               |   "A sharp tongue is the only 
Research Council Officer  IMTI-NRC   |    edge tool that grows keener 
email: john.dickinson at nrc.ca         |    with constant use." 
http://publish.uwo.ca/~jkdickin/ <http://publish.uwo.ca/~jkdickin/>      | 



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