| clip polyhedron mesh [message #90972] |
Tue, 19 May 2015 10:51  |
Guneshwar Thangjam
Messages: 9
Registered: March 2015
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Junior Member |
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Dear all,
I have a 3-dimensional polyhedron mesh where two polyhedrons are overlapped. I want to clip the polyhedron to make new polyhedrons where one portion belong the overlapping region and other non-overlapping region. If somebody knows how to do this, please let me know.
2nd option:I saw IDL's 'mesh_clip' but it is a clip using a planar surface. I dont prefer to clip using a plane, but in case if I have to use it, how I can get the coordinates of the overlapping portion?
3rd option: I also saw some discussions like polygon union/intersection ( https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/polygon$20intersection/comp.lang.idl-pvwave/uVpIUkvt-94/ Sd3NwjH-BxEJ) where Mati Maeron suggested shape_overlap.pro. But I canot find his libarry and the script. I checked in this link http://www.astro.washington.edu/docs/idl/htmlhelp/slibrary23 .html. Does anyone know where I can get his library and script?
Anyway my script/polyhedron is something like this. Dick helped me to create polyhedrons, but here I used iplot, and ipolygon.
;;1st polyhedron
x=randomu(seed,4)
y=randomu(seed,4)
z=randomu(seed,4)
xyz=[transpose(x),transpose(y),transpose(z)]
iPLOT,xyz,LINESTYLE=6,AXIS_STYLE=2,identifier='1'
QHULL,xyz,Vert
conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='1',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='SKY BLUE'
;;2nd polyhedron
x=randomu(seed,12)
y=randomu(seed,12)
z=randomu(seed,12)
xyz=[transpose(x),transpose(y),transpose(z)]
iPLOT,xyz,LINESTYLE=6,/OVERPLOT,identifier='2'
QHULL,xyz,Vert
conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='2',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='red'
Thanks,
Guni
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| Re: clip polyhedron mesh [message #90986 is a reply to message #90972] |
Wed, 20 May 2015 11:39  |
Dick Jackson
Messages: 347
Registered: August 1998
|
Senior Member |
|
|
Hi Guni,
On Tuesday, 19 May 2015 10:51:48 UTC-7, guni wrote:
> Dear all,
> I have a 3-dimensional polyhedron mesh where two polyhedrons are overlapped. I want to clip the polyhedron to make new polyhedrons where one portion belong the overlapping region and other non-overlapping region. If somebody knows how to do this, please let me know.
First, it's a much simpler problem if you know you're working with *convex* polyhedra.
A Google search on [intersection of convex polyhedra algorithm] shows that at least *somebody* knows how to do this. :-) For example:
"Finding the intersection of two convex polyhedra" from 1977:
http://www.sciencedirect.com/science/article/pii/03043975789 00518
There are lengthy algorithms that might take a lot of work to implement. Some even give solutions for intersecting convex and non-convex polyhedra.
> 2nd option:I saw IDL's 'mesh_clip' but it is a clip using a planar surface. I dont prefer to clip using a plane, but in case if I have to use it, how I can get the coordinates of the overlapping portion?
Something like this came up some time ago, and it may be the easiest way to go (assuming convex polyhedra). If you use each polygon from mesh 1 as a clipping plane into mesh 2 (and keep the correct piece each time!), when you're done, you'll be left with the intersection. This link includes another link to a useful example:
https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/intersection$20polyhedron/comp.lang.idl-pvwave/qAvnBjaws oY/JaiOeUS3KpoJ
> 3rd option: I also saw some discussions like polygon union/intersection ( https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/polygon$20intersection/comp.lang.idl-pvwave/uVpIUkvt-94/ Sd3NwjH-BxEJ) where Mati Maeron suggested shape_overlap.pro. But I canot find his libarry and the script. I checked in this link http://www.astro.washington.edu/docs/idl/htmlhelp/slibrary23 .html. Does anyone know where I can get his library and script?
I haven't tracked it down, but I'm guessing that those discussions are about polygons in 2-D, not polyhedra in 3-D.
I hope this helps!
Cheers,
-Dick
Dick Jackson Software Consulting Inc.
Victoria, BC, Canada --- http://www.d-jackson.com
P.S.: This was a nice example you gave:
> Anyway my script/polyhedron is something like this. Dick helped me to create polyhedrons, but here I used iplot, and ipolygon.
>
> ;;1st polyhedron
> x=randomu(seed,4)
> y=randomu(seed,4)
> z=randomu(seed,4)
> xyz=[transpose(x),transpose(y),transpose(z)]
> iPLOT,xyz,LINESTYLE=6,AXIS_STYLE=2,identifier='1'
> QHULL,xyz,Vert
> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='1',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='SKY BLUE'
>
> ;;2nd polyhedron
> x=randomu(seed,12)
> y=randomu(seed,12)
> z=randomu(seed,12)
> xyz=[transpose(x),transpose(y),transpose(z)]
> iPLOT,xyz,LINESTYLE=6,/OVERPLOT,identifier='2'
> QHULL,xyz,Vert
> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='2',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='red'
>
> Thanks,
> Guni
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| Re: clip polyhedron mesh [message #90987 is a reply to message #90986] |
Wed, 20 May 2015 14:48 |
Guneshwar Thangjam
Messages: 9
Registered: March 2015
|
Junior Member |
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|
On Wednesday, 20 May 2015 20:39:19 UTC+2, Dick Jackson wrote:
> Hi Guni,
>
> On Tuesday, 19 May 2015 10:51:48 UTC-7, guni wrote:
>> Dear all,
>> I have a 3-dimensional polyhedron mesh where two polyhedrons are overlapped. I want to clip the polyhedron to make new polyhedrons where one portion belong the overlapping region and other non-overlapping region. If somebody knows how to do this, please let me know.
>
> First, it's a much simpler problem if you know you're working with *convex* polyhedra.
>
> A Google search on [intersection of convex polyhedra algorithm] shows that at least *somebody* knows how to do this. :-) For example:
> "Finding the intersection of two convex polyhedra" from 1977:
> http://www.sciencedirect.com/science/article/pii/03043975789 00518
>
> There are lengthy algorithms that might take a lot of work to implement. Some even give solutions for intersecting convex and non-convex polyhedra.
>
>> 2nd option:I saw IDL's 'mesh_clip' but it is a clip using a planar surface. I dont prefer to clip using a plane, but in case if I have to use it, how I can get the coordinates of the overlapping portion?
>
> Something like this came up some time ago, and it may be the easiest way to go (assuming convex polyhedra). If you use each polygon from mesh 1 as a clipping plane into mesh 2 (and keep the correct piece each time!), when you're done, you'll be left with the intersection. This link includes another link to a useful example:
> https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/intersection$20polyhedron/comp.lang.idl-pvwave/qAvnBjaws oY/JaiOeUS3KpoJ
>
>> 3rd option: I also saw some discussions like polygon union/intersection ( https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/polygon$20intersection/comp.lang.idl-pvwave/uVpIUkvt-94/ Sd3NwjH-BxEJ) where Mati Maeron suggested shape_overlap.pro. But I canot find his libarry and the script. I checked in this link http://www.astro.washington.edu/docs/idl/htmlhelp/slibrary23 .html. Does anyone know where I can get his library and script?
>
> I haven't tracked it down, but I'm guessing that those discussions are about polygons in 2-D, not polyhedra in 3-D.
>
> I hope this helps!
>
> Cheers,
> -Dick
>
> Dick Jackson Software Consulting Inc.
> Victoria, BC, Canada --- http://www.d-jackson.com
>
> P.S.: This was a nice example you gave:
>
>> Anyway my script/polyhedron is something like this. Dick helped me to create polyhedrons, but here I used iplot, and ipolygon.
>>
>> ;;1st polyhedron
>> x=randomu(seed,4)
>> y=randomu(seed,4)
>> z=randomu(seed,4)
>> xyz=[transpose(x),transpose(y),transpose(z)]
>> iPLOT,xyz,LINESTYLE=6,AXIS_STYLE=2,identifier='1'
>> QHULL,xyz,Vert
>> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
>> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='1',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='SKY BLUE'
>>
>> ;;2nd polyhedron
>> x=randomu(seed,12)
>> y=randomu(seed,12)
>> z=randomu(seed,12)
>> xyz=[transpose(x),transpose(y),transpose(z)]
>> iPLOT,xyz,LINESTYLE=6,/OVERPLOT,identifier='2'
>> QHULL,xyz,Vert
>> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
>> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='2',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='red'
>>
>> Thanks,
>> Guni
Hi Dick
On Wednesday, 20 May 2015 20:39:19 UTC+2, Dick Jackson wrote:
> Hi Guni,
>
> On Tuesday, 19 May 2015 10:51:48 UTC-7, guni wrote:
>> Dear all,
>> I have a 3-dimensional polyhedron mesh where two polyhedrons are overlapped. I want to clip the polyhedron to make new polyhedrons where one portion belong the overlapping region and other non-overlapping region. If somebody knows how to do this, please let me know.
>
> First, it's a much simpler problem if you know you're working with *convex* polyhedra.
>
> A Google search on [intersection of convex polyhedra algorithm] shows that at least *somebody* knows how to do this. :-) For example:
> "Finding the intersection of two convex polyhedra" from 1977:
> http://www.sciencedirect.com/science/article/pii/03043975789 00518
>
> There are lengthy algorithms that might take a lot of work to implement. Some even give solutions for intersecting convex and non-convex polyhedra.
>
>> 2nd option:I saw IDL's 'mesh_clip' but it is a clip using a planar surface. I dont prefer to clip using a plane, but in case if I have to use it, how I can get the coordinates of the overlapping portion?
>
> Something like this came up some time ago, and it may be the easiest way to go (assuming convex polyhedra). If you use each polygon from mesh 1 as a clipping plane into mesh 2 (and keep the correct piece each time!), when you're done, you'll be left with the intersection. This link includes another link to a useful example:
> https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/intersection$20polyhedron/comp.lang.idl-pvwave/qAvnBjaws oY/JaiOeUS3KpoJ
>
>> 3rd option: I also saw some discussions like polygon union/intersection ( https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/polygon$20intersection/comp.lang.idl-pvwave/uVpIUkvt-94/ Sd3NwjH-BxEJ) where Mati Maeron suggested shape_overlap.pro. But I canot find his libarry and the script. I checked in this link http://www.astro.washington.edu/docs/idl/htmlhelp/slibrary23 .html. Does anyone know where I can get his library and script?
>
> I haven't tracked it down, but I'm guessing that those discussions are about polygons in 2-D, not polyhedra in 3-D.
>
> I hope this helps!
>
> Cheers,
> -Dick
>
> Dick Jackson Software Consulting Inc.
> Victoria, BC, Canada --- http://www.d-jackson.com
>
> P.S.: This was a nice example you gave:
>
>> Anyway my script/polyhedron is something like this. Dick helped me to create polyhedrons, but here I used iplot, and ipolygon.
>>
>> ;;1st polyhedron
>> x=randomu(seed,4)
>> y=randomu(seed,4)
>> z=randomu(seed,4)
>> xyz=[transpose(x),transpose(y),transpose(z)]
>> iPLOT,xyz,LINESTYLE=6,AXIS_STYLE=2,identifier='1'
>> QHULL,xyz,Vert
>> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
>> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='1',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='SKY BLUE'
>>
>> ;;2nd polyhedron
>> x=randomu(seed,12)
>> y=randomu(seed,12)
>> z=randomu(seed,12)
>> xyz=[transpose(x),transpose(y),transpose(z)]
>> iPLOT,xyz,LINESTYLE=6,/OVERPLOT,identifier='2'
>> QHULL,xyz,Vert
>> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
>> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='2',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='red'
>>
>> Thanks,
>> Guni
Hi Dick,
Thanks a lot for your help.
Well, I would like to see how MESH_CLIP works in my convex polyhedrons. I looked the link, and also the example. But, I dont know how to derive the plane coefficients in my polyhedron mesh. In the example it is defined as [1., 1., 1., 0.].
How can I derive these plane coefficients? "Plane--Input four element array describing the equation of the plane to be clipped to. The elements are the coefficients (a,b,c,d) of the equation ax+by+cz+d=0."
When I placed the mouse pointer in the plot (mesh), it shows x,y,z co-ordinates, Is it something related to the coefficients I am looking?
Thanks
Guni
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| Re: clip polyhedron mesh [message #90988 is a reply to message #90987] |
Thu, 21 May 2015 00:09 |
Dick Jackson
Messages: 347
Registered: August 1998
|
Senior Member |
|
|
guni wrote on 2015-05-20 2:48pm:
> On Wednesday, 20 May 2015 20:39:19 UTC+2, Dick Jackson wrote:
>> Hi Guni,
>>
>> On Tuesday, 19 May 2015 10:51:48 UTC-7, guni wrote:
>>> Dear all, I have a 3-dimensional polyhedron mesh where two polyhedrons
>>> are overlapped. I want to clip the polyhedron to make new polyhedrons
>>> where one portion belong the overlapping region and other non-overlapping
>>> region. If somebody knows how to do this, please let me know.
>>
>> First, it's a much simpler problem if you know you're working with *convex*
>> polyhedra.
>>
>> A Google search on [intersection of convex polyhedra algorithm] shows that
>> at least *somebody* knows how to do this. :-) For example: "Finding the
>> intersection of two convex polyhedra" from 1977:
>> http://www.sciencedirect.com/science/article/pii/03043975789 00518
>>
>> There are lengthy algorithms that might take a lot of work to implement.
>> Some even give solutions for intersecting convex and non-convex polyhedra.
> Hi Dick
>
> On Wednesday, 20 May 2015 20:39:19 UTC+2, Dick Jackson wrote:
>> Hi Guni,
>>
>> On Tuesday, 19 May 2015 10:51:48 UTC-7, guni wrote:
>>> Dear all, I have a 3-dimensional polyhedron mesh where two polyhedrons
>>> are overlapped. I want to clip the polyhedron to make new polyhedrons
>>> where one portion belong the overlapping region and other non-overlapping
>>> region. If somebody knows how to do this, please let me know.
>>
>> First, it's a much simpler problem if you know you're working with *convex*
>> polyhedra.
>>
>> [...]
>>
>>> 2nd option:I saw IDL's 'mesh_clip' but it is a clip using a planar
>>> surface. I dont prefer to clip using a plane, but in case if I have to
>>> use it, how I can get the coordinates of the overlapping portion?
>>
>> Something like this came up some time ago, and it may be the easiest way to
>> go (assuming convex polyhedra). If you use each polygon from mesh 1 as a
>> clipping plane into mesh 2 (and keep the correct piece each time!), when
>> you're done, you'll be left with the intersection. This link includes
>> another link to a useful example:
>> https://groups.google.com/forum/#!searchin/comp.lang.idl-pvw ave/intersection$20polyhedron/comp.lang.idl-pvwave/qAvnBjaws oY/JaiOeUS3KpoJ
>>
>> [...]
>>
>> I hope this helps!
>>
>> Cheers, -Dick
>>
>> Dick Jackson Software Consulting Inc. Victoria, BC, Canada ---
>> http://www.d-jackson.com
>>
>> P.S.: This was a nice example you gave:
>>
>>> Anyway my script/polyhedron is something like this. Dick helped me to
>>> create polyhedrons, but here I used iplot, and ipolygon.
>>>
>>> ;;1st polyhedron x=randomu(seed,4) y=randomu(seed,4) z=randomu(seed,4)
>>> xyz=[transpose(x),transpose(y),transpose(z)]
>>> iPLOT,xyz,LINESTYLE=6,AXIS_STYLE=2,identifier='1' QHULL,xyz,Vert
>>> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
>>> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='1',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='SKY
>>> BLUE'
>>>
>>> ;;2nd polyhedron x=randomu(seed,12) y=randomu(seed,12)
>>> z=randomu(seed,12) xyz=[transpose(x),transpose(y),transpose(z)]
>>> iPLOT,xyz,LINESTYLE=6,/OVERPLOT,identifier='2' QHULL,xyz,Vert
>>> conn=[REPLICATE(3,[1,N_ElEMENTS(Vert)/3]),Vert]
>>> iPOLYGON,xyz,/DATA,CONNECTIVITY=conn,visualization='2',trans parency=50,/FILL_BACKGROUND,FILL_COLOR='red'
>>>
>>>
>>>
Thanks,
>>> Guni
>
> Hi Dick, Thanks a lot for your help. Well, I would like to see how MESH_CLIP
> works in my convex polyhedrons. I looked the link, and also the example. But,
> I dont know how to derive the plane coefficients in my polyhedron mesh. In
> the example it is defined as [1., 1., 1., 0.]. How can I derive these plane
> coefficients? "Plane--Input four element array describing the equation of the
> plane to be clipped to. The elements are the coefficients (a,b,c,d) of the
> equation ax+by+cz+d=0." When I placed the mouse pointer in the plot (mesh),
> it shows x,y,z co-ordinates, Is it something related to the coefficients I am
> looking? Thanks Guni
>
Right, that's not trivial. I had found the magic at
http://paulbourke.net/geometry/pointlineplane/
... and a function implementing this (and more) is below.
For each triangle in the mesh, you can use this routine to get the coefficients:
abcd = PlaneCoeffs([[x0,y0,z0],[x1,y1,z1],[x2,y2,z2]])
You should double-check that the resulting value results in the correct side of
the plane being used. If it's wrong, then do one of these:
- send points in reordered as [[x0,y0,z0],[x2,y2,z2],[x1,y1,z1]], or
- use -(abcd) instead of abcd
Let me know if that works out!
Cheers,
-Dick
Dick Jackson Software Consulting Inc. -- www.d-jackson.com
;-----
; PlaneCoeffs
;+
; :Description:
; From the input data provided in one of several forms, return the
; coefficients that define the plane.
;
; :Returns:
; Floating-point vector [a,b,c,d] defining the plane *ax + by + cz + d = 0*
;
; :Keywords:
; Points : in, optional, type=numeric 1-D or 2-D array
; Either:
; - One point [x,y,z] on the desired plane, requiring one
; of XYangle, XZangle, YZangle or NormalVector to be provided, or:
; - Three points [[x0,y0,z0],[x1,y1,z1],[x2,y2,z2]] that
; fully define the plane.
; XYangle : in, optional, type=numeric scalar
; For a plane parallel to the Z axis, the angle between the Y=0 line and
; the desired plane (in degrees, counter-clockwise)
; XZangle : in, optional, type=numeric scalar
; For a plane parallel to the Y axis, the angle between the Z=0 line and
; the desired plane (in degrees, counter-clockwise)
; YZangle : in, optional, type=numeric scalar
; For a plane parallel to the X axis, the angle between the Y=0 line and
; the desired plane (in degrees, counter-clockwise)
; NormalVector : in, optional, type=numeric 1-D array
; A 3-element vector (x,y,z) describing the normal to the desired plane
;
; :Examples:
; Find the equation of the plane that passes through the points
; [1,1,1], [-1,1,0], [2,0,3]
; IDL> Print, PlaneCoeffs(Points=[[1,1,1], [-1,1,0], [2,0,3]])
; -1 3 2 -4
; (or, -x + 3y - 2z - 4 = 0)
; IDL> Print, PlaneCoeffs(Points=[0,0,0], YZAngle=30)
; 0.000000 0.500000 -0.866025 -0.000000
; IDL> Print, PlaneCoeffs(Points=[1,2,3], NormalVector=[4,5,6])
; 4 5 6 -32
;
; :Author:
; Dick Jackson Software Consulting Inc. -- www.d-jackson.com
;
; :History:
; 2009-10-02 djackson
; First revision, partly from former PlaneFrom3Points.pro
; 2009-10-05 djackson
; New: Keyword NormalVector
; Doc: Improved comments, changed to RST format
; 2015-05-20 djackson
; Doc: Improved docs
;-
;*********************************************************** ******************;
; Copyright (c) 2015, by Dick Jackson Software Consulting Inc. ;
; All rights reserved. ;
; ;
; Redistribution and use in source and binary forms, with or without ;
; modification, are permitted provided that the following conditions are met:;
; ;
; * Redistributions of source code must retain the above copyright ;
; notice, this list of conditions and the following disclaimer. ;
; * Redistributions in binary form must reproduce the above copyright ;
; notice, this list of conditions and the following disclaimer in the ;
; documentation and/or other materials provided with the distribution. ;
; * Neither the name of Dick Jackson Software Consulting Inc. nor the ;
; names of its contributors may be used to endorse or promote products ;
; derived from this software without specific prior written permission.;
; ;
; THIS SOFTWARE IS PROVIDED BY DICK JACKSON SOFTWARE CONSULTING INC. "AS IS" ;
; AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ;
; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ;
; ARE DISCLAIMED. IN NO EVENT SHALL DICK JACKSON SOFTWARE CONSULTING INC. ;
; BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR ;
; CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF ;
; SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; LOSS OF USE, ;
; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY ;
; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT ;
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF ;
; THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ;
;*********************************************************** ******************;
FUNCTION PlaneCoeffs, Points=points, XYangle=xyAngle, XZangle=xzAngle, $
YZangle=yzAngle, NormalVector=normalVector
COMPILE_OPT IDL2 ; Integers default to 32-bit and indexing requires use of []
CASE 1B OF
;; Three points
Array_Equal(Size(points, /Dimensions), [3, 3]) AND $
(N_Elements(xyAngle)+N_Elements(xzAngle)+N_Elements(yzAngle) ) EQ 0: $
BEGIN
;; Method from http://paulbourke.net/geometry/pointlineplane/
p1 = points[*, 0] & p2 = points[*, 1] & p3 = points[*, 2]
x1 = p1[0] & y1 = p1[1] & z1 = p1[2]
x2 = p2[0] & y2 = p2[1] & z2 = p2[2]
x3 = p3[0] & y3 = p3[1] & z3 = p3[2]
a = y1*(z2 - z3) + y2*(z3 - z1) + y3*(z1 - z2)
b = z1*(x2 - x3) + z2*(x3 - x1) + z3*(x1 - x2)
c = x1*(y2 - y3) + x2*(y3 - y1) + x3*(y1 - y2)
d = -( x1*(y2*z3 - y3*z2) + x2*(y3*z1 - y1*z3) + x3*(y1*z2 - y2*z1) )
END ;; Three points case
;; One point and an angle (one of XYangle, XZangle or YZangle)
N_Elements(points) EQ 3 AND N_Elements(xyAngle) EQ 1: BEGIN
a = Cos((xyAngle-90) * !DtoR)
b = Sin((xyAngle-90) * !DtoR)
c = 0
d = -(a*points[0]+b*points[1])
END ;; One point and XYangle
N_Elements(points) EQ 3 AND N_Elements(xzAngle) EQ 1: BEGIN
a = Cos((xzAngle-90) * !DtoR)
c = Sin((xzAngle-90) * !DtoR)
b = 0
d = -(a*points[0]+c*points[2])
END ;; One point and XZangle
N_Elements(points) EQ 3 AND N_Elements(yzAngle) EQ 1: BEGIN
b = Cos((yzAngle-90) * !DtoR)
c = Sin((yzAngle-90) * !DtoR)
a = 0
d = -(b*points[1]+c*points[2])
END ;; One point and YZangle
N_Elements(points) EQ 3 AND N_Elements(normalVector) EQ 3: BEGIN
a = normalVector[0]
b = normalVector[1]
c = normalVector[2]
d = -(a*points[0]+b*points[1]+c*points[2])
END ;; One point and NormalVector
ENDCASE ;; of different input options
Return, [a, b, c, d]
END
;-----
--
Cheers,
-Dick
Dick Jackson Software Consulting Inc.
Victoria, BC, Canada
www.d-jackson.com
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