Ordering 3dpoints ?

Dan Rathbun

What about about using a temporary BouningBox around the 4 pts.
Each pt would lie on one of the BB's planes. 2 of the BB's planes would not have a point.
Either the vertical planes will have the pts, or the top and bottom and 2 side planes will have the points.

Chris Fullmer

I can only manage to describe this in 2d, so you get to implement it onto any 3d plane. I tihnk it is similar to what Fredo suggested - his is probably faster. Mine requires re-calculating on each point. But mine works to find the convex face that bounds MANY points if needed.

Get the point in the most negative x location. Then get the angle between the vector -1,0,0 and the vector from your point to all other points. The smallest angle is the next point in the convex face. You have to make sure you are always getting the angle going in the correct direction (clockwise or counter-clockwise). Then use the previous vector as the new base vector when you go to test for the next point.

I made a video that shows it. Think of the protractor as doing the testing. It rotates until it finds the next point to use - it is the point with the smallest angle.

There is no sound.
[flash=638,509:26c6u44v]http://www.chrisfullmer.com/forums/convex_face_finder.swf[/flash:26c6u44v]

Jim

Start by looking at the cross product of each vertex's edge vectors.


model = Sketchup.active_model
entities = model.entities
selection = model.selection

pts = [  [0, 0], [0, 1], [1, 1], [1, 0] ]
pts2 = [ pts[0], pts[2], pts[1], pts[3] ]

g1 = entities.add_group
g1.entities.add_face pts
pts.each_with_index{|pt, i| g1.entities.add_text((i+1).to_s, pt)}
g1.name = "Normal"

g2 = entities.add_group
g2.entities.add_face pts2
g2.name = "Swapped"
pts2.each_with_index{|pt, i| g2.entities.add_text((i+1).to_s, pt)}

def show_cross(ents, ary)
  p1, p2, p3, p4 = ary
  n1 = ((p1.vector_to p4) * (p1.vector_to p2)).normalize
  n2 = ((p2.vector_to p1) * (p2.vector_to p3)).normalize
  n3 = ((p3.vector_to p2) * (p3.vector_to p4)).normalize
  n4 = ((p4.vector_to p3) * (p4.vector_to p1)).normalize
  ents.add_line(p1, p1.offset(n1))
  ents.add_line(p2, p2.offset(n2))
  ents.add_line(p3, p3.offset(n3))
  ents.add_line(p4, p4.offset(n4))
end

show_cross(g1.entities, pts)
show_cross(g2.entities, pts2)

TIG

http://en.wikipedia.org/wiki/Graham_scan ?
Ensures 'convex' shapes...

thomthom

@tig said:

http://en.wikipedia.org/wiki/Graham_scan ?
Ensures 'convex' shapes...

I got an implementation of Grahams Scan in TT_Lib (version 1)
From geom2d.rb

<span class="syntaxdefault"><br /></span><span class="syntaxcomment"># Graham's Scan<br /># Computational Geometry Algorythms and Appliations (ISBN-10; 3540779736)<br /># Chapter 1.1<br />#<br /># @param [Array<Geom;;Point3d>] points<br /># @return [Array<Geom;;Point3d>]<br /># @since 1.1.0<br /></span><span class="syntaxdefault">def self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">convex_hull</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">  return nil if points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword"><</span><span class="syntaxdefault"> 2<br />  <br />  points </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort_points_by_x_y</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">  <br />  l_upper </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">[</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">],</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">]</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">  2</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">upto</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">-</span><span class="syntaxdefault"> 1</span><span class="syntaxkeyword">)</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">{</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">|</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">|<br /></span><span class="syntaxdefault">    l_upper </span><span class="syntaxkeyword"><<</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">    while l_upper</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">></span><span class="syntaxdefault"> 2 </span><span class="syntaxkeyword">&&</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">!</span><span class="syntaxdefault">self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">right_turn</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">l_upper</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">last</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">3</span><span class="syntaxkeyword">))<br /></span><span class="syntaxdefault">      l_upper</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(-</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    end<br />  </span><span class="syntaxkeyword">}<br /></span><span class="syntaxdefault">  <br />  l_lower </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">[</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[-</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">],</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[-</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">]</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">  </span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">-</span><span class="syntaxdefault"> 3</span><span class="syntaxkeyword">).</span><span class="syntaxdefault">downto</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">)</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">{</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">|</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">|<br /></span><span class="syntaxdefault">    l_lower </span><span class="syntaxkeyword"><<</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">    while l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">></span><span class="syntaxdefault"> 2 </span><span class="syntaxkeyword">&&</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">!</span><span class="syntaxdefault">self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">right_turn</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">last</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">3</span><span class="syntaxkeyword">))<br /></span><span class="syntaxdefault">      l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(-</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    end<br />  </span><span class="syntaxkeyword">}<br /></span><span class="syntaxdefault">  l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">  l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(-</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">  <br />  return l_upper </span><span class="syntaxkeyword">+</span><span class="syntaxdefault"> l_lower<br />end<br /><br /><br /></span><span class="syntaxcomment"># Lexicographic order x, y<br />#<br /># @param [Array<Geom;;Point3d>] points<br /># @return [Array<Geom;;Point3d>]<br /># @since 1.1.0<br /></span><span class="syntaxdefault">def self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort_points_by_x_y</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">  return points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort </span><span class="syntaxkeyword">{</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">|</span><span class="syntaxdefault">a</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">b</span><span class="syntaxkeyword">|</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">(</span><span class="syntaxdefault">a</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x</span><span class="syntaxkeyword">==</span><span class="syntaxdefault">b</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x</span><span class="syntaxkeyword">)</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">?</span><span class="syntaxdefault"> a</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">y </span><span class="syntaxkeyword"><=></span><span class="syntaxdefault"> b</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">y </span><span class="syntaxkeyword">;</span><span class="syntaxdefault"> a</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x </span><span class="syntaxkeyword"><=></span><span class="syntaxdefault"> b</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x </span><span class="syntaxkeyword">}<br /></span><span class="syntaxdefault">end<br /></span>

Didier Bur

Thanks TIG and TT, I was just starting coding Graham's scan, this will save me time.
Left turn/right turn and cross products will do the trick I presume.

What's all that for: I'm working on subdivision curves and surfaces: Catmull-Clark, Loop, Doo-Sabin, Peters-Reif, Kobbelt, Chaikin, and others. Peters-Reif seemed too me the simplest algorithm but turned out to be one of the most complex, comparing to Catmull which I have coded in an hour or so.
I'm facing the CW/CCW and ordering problem, and the 'correctly orienting faces' problem. That's fun

@TT: didn't you encounter problems with == method when comparing Floats (in (a.x==b.x) for instance) ?
I've come across this:

plane1=Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[2])
plane2=(Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[3]))
return plane1==plane2

Assuming the 4 3dPoints are coplanar, this always return false. I had to code another method 'isEqual?' for the Float class that compares with a tolerance of 1 to the power of -10 to get correct results when comparing such arrays of floats.

thomthom

@didier bur said:

@TT: didn't you encounter problems with == method when comparing Floats (in (a.x==b.x) for instance) ?

Good point. I haven't tested it that much, I just ported some pseudo code which I read in a book.
One should probably do a tolerance comparison.

[quote="Didier Bur"]


    plane1=Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[2])
    plane2=(Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[3]))
    return plane1==plane2

<span class="syntaxdefault"><br /></span><span class="syntaxcomment">#&nbsp;Check&nbsp;if&nbsp;all&nbsp;points&nbsp;in&nbsp;the&nbsp;array&nbsp;are&nbsp;on&nbsp;the&nbsp;same&nbsp;plane.<br />#<br />#&nbsp;@todo&nbsp;Ensure&nbsp;that&nbsp;the&nbsp;first&nbsp;three&nbsp;points&nbsp;are&nbsp;not&nbsp;co-linear.<br />#<br />#&nbsp;@param&nbsp;[Array<Geom;;Point3d>]&nbsp;points<br />#<br />#&nbsp;@since&nbsp;2.0.0<br /></span><span class="syntaxdefault">def&nbsp;self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">planar_points</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br />&nbsp;&nbsp;return&nbsp;</span><span class="syntaxdefault">false&nbsp;</span><span class="syntaxkeyword">if&nbsp;</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length&nbsp;</span><span class="syntaxkeyword"><&nbsp;</span><span class="syntaxdefault">3<br />&nbsp;&nbsp;v1&nbsp;</span><span class="syntaxkeyword">=&nbsp;</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">].</span><span class="syntaxdefault">vector_to</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">])<br />&nbsp;&nbsp;</span><span class="syntaxdefault">v2&nbsp;</span><span class="syntaxkeyword">=&nbsp;</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">].</span><span class="syntaxdefault">vector_to</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">])<br />&nbsp;&nbsp;return&nbsp;</span><span class="syntaxdefault">false&nbsp;unless&nbsp;v1</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">valid</span><span class="syntaxkeyword">?&nbsp;&&&nbsp;</span><span class="syntaxdefault">v2</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">valid</span><span class="syntaxkeyword">?<br />&nbsp;&nbsp;</span><span class="syntaxdefault">vector&nbsp;</span><span class="syntaxkeyword">=&nbsp;</span><span class="syntaxdefault">v1&nbsp;</span><span class="syntaxkeyword">*&nbsp;</span><span class="syntaxdefault">v2<br />&nbsp;&nbsp;plane&nbsp;</span><span class="syntaxkeyword">=&nbsp;[&nbsp;</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">],&nbsp;</span><span class="syntaxdefault">vector&nbsp;</span><span class="syntaxkeyword">]<br />&nbsp;&nbsp;</span><span class="syntaxdefault">3.upto</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length</span><span class="syntaxkeyword">-</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">)&nbsp;{&nbsp;|</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">|<br />&nbsp;&nbsp;&nbsp;&nbsp;return&nbsp;</span><span class="syntaxdefault">false&nbsp;unless&nbsp;points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">].</span><span class="syntaxdefault">on_plane</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">plane</span><span class="syntaxkeyword">)<br />&nbsp;&nbsp;}<br />&nbsp;&nbsp;return&nbsp;</span><span class="syntaxdefault">true<br />end<br /></span>

thomthom

@didier bur said:

What's all that for: I'm working on subdivision curves and surfaces: Catmull-Clark, Loop, Doo-Sabin, Peters-Reif, Kobbelt, Chaikin, and others. Peters-Reif seemed too me the simplest algorithm but turned out to be one of the most complex, comparing to Catmull which I have coded in an hour or so.

I wish I could understand algorithm formulas. I always need to search up a pseudo code version, or an implementation in another language to work it out.

thomthom

@didier bur said:

@TT: didn't you encounter problems with == method when comparing Floats (in (a.x==b.x) for instance) ?

Actually, Point3d.x, Point3d.y and Point3d.z return Length objects. They have built in tolerances - same as SU's.
You can easily get in trouble with unpredictable results if you're not 100% sure if you're dealing with Floats or Lengths.

Didier Bur

@unknownuser said:

I wish I could understand algorithm formulas. I always need to search up a pseudo code version, or an implementation in another language to work it out.

Me too. When I speak of 'algorithm' I mean pseudo-code or (even better) natural language

Here is my snippet for coplanarity test of 4 points (can be extended to any number of points):

# Given a set of 4 3dPoints, return true if coplanar, or false
	def quadPointsCoplanar?(pArray)
		return (Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[2]).isEqual?(Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[3])))
	end

Where Array of floats comparison method must be 'aliased' with isEqual?

class Array
	def isEqual?(otherArray)
		self.each_index { |i| return false if self[i].isNotEqual(otherArray[i]) }
		return true
	end
end

and where == method for floats must be aliased with isNotEqual()

class Float
	def isNotEqual(value)
		delta = self - value
		return ((delta > Math;;EPSILON) or (delta < -Math;;EPSILON))
	end
end

and finaly requires a constant

Math.const_set("EPSILON", 1.0e-10)

thomthom

I came across a very good site on the topic of floating precision: http://floating-point-gui.de/
Comparison with tolerance is a bit more complex in order to account for the various pit-falls.

http://floating-point-gui.de/errors/comparison/

thomthom

Ooops! Seems that I forgot to post all required methods:

<span class="syntaxdefault"><br />module TT_Lib<br /> module Geom2D<br />  <br />  </span><span class="syntaxcomment"># Graham's Scan<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># Computational Geometry Algorythms and Appliations (ISBN-10; 3540779736)<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># Chapter 1.1<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment">#<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @param [Array<Geom;;Point3d>] points<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @return [Array<Geom;;Point3d>]<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @since 1.1.0<br /></span><span class="syntaxdefault">  def self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">convex_hull</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    return nil if points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword"><</span><span class="syntaxdefault"> 2<br />    <br />    points </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort_points_by_x_y</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    <br />    l_upper </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">[</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">],</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">]</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">    2</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">upto</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">-</span><span class="syntaxdefault"> 1</span><span class="syntaxkeyword">)</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">{</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">|</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">|<br /></span><span class="syntaxdefault">      l_upper </span><span class="syntaxkeyword"><<</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">      while l_upper</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">></span><span class="syntaxdefault"> 2 </span><span class="syntaxkeyword">&&</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">!</span><span class="syntaxdefault">self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">right_turn</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">l_upper</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">last</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">3</span><span class="syntaxkeyword">))<br /></span><span class="syntaxdefault">        l_upper</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(-</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">      end<br />    </span><span class="syntaxkeyword">}<br /></span><span class="syntaxdefault">    <br />    l_lower </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">[</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[-</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">],</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[-</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">]</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">    </span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">-</span><span class="syntaxdefault"> 3</span><span class="syntaxkeyword">).</span><span class="syntaxdefault">downto</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">)</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">{</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">|</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">|<br /></span><span class="syntaxdefault">      l_lower </span><span class="syntaxkeyword"><<</span><span class="syntaxdefault"> points</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">i</span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">      while l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">length </span><span class="syntaxkeyword">></span><span class="syntaxdefault"> 2 </span><span class="syntaxkeyword">&&</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">!</span><span class="syntaxdefault">self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">right_turn</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">last</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">3</span><span class="syntaxkeyword">))<br /></span><span class="syntaxdefault">        l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(-</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">      end<br />    </span><span class="syntaxkeyword">}<br /></span><span class="syntaxdefault">    l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    l_lower</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">delete_at</span><span class="syntaxkeyword">(-</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    <br />    return l_upper </span><span class="syntaxkeyword">+</span><span class="syntaxdefault"> l_lower<br />  end<br />  <br />  <br />  </span><span class="syntaxcomment"># @param [Array<Geom;;Point3d>] points<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @return [Array<Geom;;Point3d>]<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @since 1.1.0<br /></span><span class="syntaxdefault">  def self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort_points_by_x</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    return points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort </span><span class="syntaxkeyword">{</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">|</span><span class="syntaxdefault">a</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">b</span><span class="syntaxkeyword">|</span><span class="syntaxdefault"> a</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x </span><span class="syntaxkeyword"><=></span><span class="syntaxdefault"> b</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x </span><span class="syntaxkeyword">}<br /></span><span class="syntaxdefault">  end<br />  <br />  <br />  </span><span class="syntaxcomment"># Lexicographic order x, y<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment">#<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @param [Array<Geom;;Point3d>] points<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @return [Array<Geom;;Point3d>]<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @since 1.1.0<br /></span><span class="syntaxdefault">  def self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort_points_by_x_y</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    return points</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">sort </span><span class="syntaxkeyword">{</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">|</span><span class="syntaxdefault">a</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">b</span><span class="syntaxkeyword">|</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">(</span><span class="syntaxdefault">a</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x</span><span class="syntaxkeyword">==</span><span class="syntaxdefault">b</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x</span><span class="syntaxkeyword">)</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">?</span><span class="syntaxdefault"> a</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">y </span><span class="syntaxkeyword"><=></span><span class="syntaxdefault"> b</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">y </span><span class="syntaxkeyword">;</span><span class="syntaxdefault"> a</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x </span><span class="syntaxkeyword"><=></span><span class="syntaxdefault"> b</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x </span><span class="syntaxkeyword">}<br /></span><span class="syntaxdefault">  end<br />  <br />  <br />  </span><span class="syntaxcomment"># @param [Array<Geom;;Point3d>] points array of 3 +Geom;;Point3d+ objects.<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @since 1.1.0 - Renamed from +.right_turn+ to +.right_turn?+ at version 1.2.0<br /></span><span class="syntaxdefault">  def self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">right_turn</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">points</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">    p</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> q</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> r </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> points<br />    array </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">[</span><span class="syntaxdefault"> 1</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> p</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> p</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">y</span><span class="syntaxkeyword">,<br /></span><span class="syntaxdefault">          1</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> q</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> q</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">y</span><span class="syntaxkeyword">,<br /></span><span class="syntaxdefault">          1</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> r</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">x</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> r</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">y </span><span class="syntaxkeyword">]<br /></span><span class="syntaxdefault">    return self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">determinant_3x3</span><span class="syntaxkeyword">(array)</span><span class="syntaxdefault"> </span><span class="syntaxkeyword"><</span><span class="syntaxdefault"> 0.0<br />  end<br />  <br />  </span><span class="syntaxcomment"># @param [Array<Number>] array<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @return [Number]<br /></span><span class="syntaxdefault">  </span><span class="syntaxcomment"># @since 1.1.0<br /></span><span class="syntaxdefault">  def self</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">determinant_3x3</span><span class="syntaxkeyword">(array)<br /></span><span class="syntaxdefault">    a</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">b</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">c</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">d</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">e</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">f</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">g</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">h</span><span class="syntaxkeyword">,</span><span class="syntaxdefault">i </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> array<br />    return a</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">e</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">i </span><span class="syntaxkeyword">-</span><span class="syntaxdefault"> a</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">f</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">h </span><span class="syntaxkeyword">+</span><span class="syntaxdefault"> b</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">f</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">g </span><span class="syntaxkeyword">-</span><span class="syntaxdefault"> b</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">d</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">i </span><span class="syntaxkeyword">+</span><span class="syntaxdefault"> c</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">d</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">h </span><span class="syntaxkeyword">-</span><span class="syntaxdefault"> c</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">e</span><span class="syntaxkeyword">*</span><span class="syntaxdefault">g<br />  end<br />  <br /> end </span><span class="syntaxcomment"># module Geom2D<br /></span><span class="syntaxdefault">end </span><span class="syntaxcomment"># module TT_Lib<br /></span><span class="syntaxdefault"> </span>

fredo6

@didier bur said:

Here is my snippet for coplanarity test of 4 points (can be extended to any number of points):

# Given a set of 4 3dPoints, return true if coplanar, or false
> 	def quadPointsCoplanar?(pArray)
> 		return (Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[2]).isEqual?(Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[3])))
> 	end

I had a method for that in LibFredo6. Here is the code (slightly modified in order to return the plane or nil)


#Check if a set of points are coplanar
#  --> Return the plane or nil
def G6.points_coplanar?(pts)
	n = pts.length
	return nil if n < 3
	return Geom.fit_plane_to_points(pts) if n == 3
	
	n1 = [n / 2, 3].max
	n2 = [n - n1, 3].max
	plane1 = Geom.fit_plane_to_points *(pts[0..n1-1])
	plane2 = Geom.fit_plane_to_points *(pts[n-n2..n-1])
	normal1 = Geom;;Vector3d.new *plane1[0..2]
	normal2 = Geom;;Vector3d.new *plane2[0..2]
	(normal1.parallel?(normal2) && pts[0].on_plane?(plane2)) ? plane1 ; nil
end

Fredo

PS: I don't think it is a good idea to extend the Array and Float ruby classes. Better used a specific private method


def compare_float_arrays(array1, array2, epsilon)
   for i in 0..array1.length
       return false if (array1[i] - array2[i]).abs > epsilon
   end
   true
end

thomthom

@unknownuser said:

PS: I don't think it is a good idea to extend the Array and Float ruby classes. Better used a specific private method

Ditto. Any Ruby and Sketchup base classes. There's been a few cases with clashes over methods like this.

Dan Rathbun

@unknownuser said:

PS: I don't think it is a good idea to extend the Array and Float ruby classes. Better used a specific private method

And I was going to say the same... and also suggest a compare method with multiple arguemnts.

1) Never extend Ruby base classes, solely to solve one coding challenge that only applies to your project. Use a custom subclass and extend that subclass.
IF you absolutely must have an instance method that acts on the object... then you should create a custom Array subclass and/or a custom Float subclass, and then add your custom methods to those custom classes.

2) Custom classes are never defined at the top level (only Ruby base classes are.) Just because someone else does it, does not mean you should.
Just as Google defined their custom classes inside the modules (Sketchup, UI, Geom,) you should define any custom classes inside your Toplevel module (but they can be nested inside submodules if you wish.)

3) There is an alternative to extending base classes or creating a custom subclass. It's called extending an object. You create a mixin module that has your custom method(s) in it, written as instance methods (not module methods.) Then when you have an INSTANCE object, you extend that specific object via:
require 'epsilon_compare.rb' my_array.extend(EpsilonCompare)
Then that specific array (and only that array,) will have your custom method(s). This way you do not interfere with the rest of the Ruby world's use of the Array class.

4) Sometimes it is necessary to extend or fix a base class for everyone, but this should be done with community approval... and likely for temporary use only, until either the SU API or the Ruby Core can be updated to include the fix or feature. (I'm actually working on such a global fix right now.. but I will post it in the SKX forum for comment and testing. I will not just release it to the Sketchup world, unitl it's tested, proven and approved.)
~

Dan Rathbun

Although == is often overriden in custom subclasses (to do type conversion etc.,) .eql?() is usually not overriden, and retains the original finctionality of the == inherited from the superclass.

Also .equal?() is NEVER overriden! (It's a really big no no.)
~

Jim

moved - ot.

Dan Rathbun

@didier bur said:

Here is my snippet for coplanarity test of 4 points (can be extended to any number of points):

# Given a set of 4 3dPoints, return true if coplanar, or false
> 	def quadPointsCoplanar?(pArray)
> 		return (Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[2]).isEqual?(Geom.fit_plane_to_points(pArray[0],pArray[1],pArray[3])))
> 	end

Will this work to simplify things ?

<span class="syntaxdefault"></span><span class="syntaxcomment"># Given a set of 4 3dPoints, return true if coplanar, or false<br /></span><span class="syntaxdefault">    def quadPointsCoplanar</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">pArray</span><span class="syntaxkeyword">)<br /></span><span class="syntaxdefault">        return </span><span class="syntaxkeyword">(</span><span class="syntaxdefault">Geom</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">fit_plane_to_points</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">pArray</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">],</span><span class="syntaxdefault">pArray</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">],</span><span class="syntaxdefault">pArray</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">2</span><span class="syntaxkeyword">]).</span><span class="syntaxdefault">eql</span><span class="syntaxkeyword">?(</span><span class="syntaxdefault">Geom</span><span class="syntaxkeyword">.</span><span class="syntaxdefault">fit_plane_to_points</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">pArray</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">0</span><span class="syntaxkeyword">],</span><span class="syntaxdefault">pArray</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">1</span><span class="syntaxkeyword">],</span><span class="syntaxdefault">pArray</span><span class="syntaxkeyword">[</span><span class="syntaxdefault">3</span><span class="syntaxkeyword">])))<br /></span><span class="syntaxdefault">    end</span>

I have no problem on Ruby 1.8.6 comparing floats that are very close:
1.0000000001 == 1.0000000002 false 1.0000000001 == 1.0000000001 true

fredo6

I don't think eql? or any float comparison method would work, because the plane defined by [a0, a1, a2, a3] is the same as the one defined by [2 * a0, 2 * a1, 2 * a2, 2 * a3] or any other multiplying factor.

It may be however that Geom.fit_plane_to_points normalizes the returned array, but it is not sure.

So to be on the safe side, both for the precision and for the comparison, I would recommend to compare the planes A[a0, a1, a2, a3] and B[b0, b1, b2, b3] by:

checking if their normals [a0, a1, a2] and [b0, b1, b2] are parallel. SU will answer true or false taking into account the float precision
checking if the first point in the set of points is located on the second plane B.

So, in Dider's example:


def quadPointsCoplanar?(pArray)
   planeA = Geom.fit_plane_to_points pArray[0], pArray[1], pArray[2]
   planeB = Geom.fit_plane_to_points pArray[1], pArray[2], pArray[3]
   normalA = Geom;;Vector3d.new *planeA[0..2]
   normalB = Geom;;Vector3d.new *planeB[0..2]
   normalA.parallel?(normalB) && pArray[0].on_plane?(planeB)
end

Now for 4 points which are different and non-aligned, it is of course easier to do


def quadPointsCoplanar?(pArray)
    planeA = Geom.fit_plane_to_points pArray[0], pArray[1], pArray[2]
    pArray[3].on_plane?(planeA)
end

Fredo

PS to Dan: very instructive your tuto on subclassing, really! Thanks.

Didier Bur

@Dan:
@unknownuser said:

Will this work to simplify things ?
No, it doesn't work.
@all: OK for not adding methods to base classes or SU classes. Module/sub-module stuffs are annoying to code (although the mixin mecanism is fun...) but far more secure.
@tt: your Graham's scan works on every common or horizontal face, but not on vertical faces (I mean sets of 4 points that are in a main vertical plane (red-blue), (green-blue), see pic. I suppose that this is due to points having same X and same Y are not sorted correctly. I've tried to apply a transformation to each point before sorting, and apply the inverse transformation after, but no luck.
This transformation was taking the normal of the plane of the 4 points as the Z axis, so the 4 points were virtually in a horizontal plane to be correctly handled by Graham, which is '2D'.)