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Alternative to angle_between?

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  • T Offline
    thomthom
    last edited by 23 May 2009, 20:32

    If the red and blue vector where both 90 degrees from the black vector vZ returned (0,0,0) which then give me 0.0 for v1 and v2...
    I think I've gotten something wrong...

    (Currently reading up on vectors on Wiki...goes a bit over my head. Any recommended starting material?)

    Thomas Thomassen β€” SketchUp Monkey & Coding addict
    List of my plugins and link to the CookieWare fund

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    • R Offline
      remus
      last edited by 23 May 2009, 20:40

      this is quite good, as long as you skim over the first paragraph. http://mathworld.wolfram.com/Vector.html

      http://remusrendering.wordpress.com/

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      • T Offline
        thomthom
        last edited by 23 May 2009, 21:31

        @unknownuser said:

        You have to choose a Z direction (perpendicular to the plane of the two vectors, in order ot orient your angles.
        Otherwise it is normal that you get the same value (just imagine you look at your picture from the back!).

        Then you make a difference by the sign of (vec1 * vec2) % vecZ

        Fredo

        Ok... I'm not 100% sure if I understand this. But this is what I tried:

        e1 = base vector e2 = left vector e3 = right vector

        
        vZ = e2 * e3 # returns (0, 0, -0.5)
        v1 = (e1 * e2) % vZ # returns 7.41461947099021
        v2 = (e1 * e3) % vZ # returns -7.41461947099021
        
        

        That does give me a positive and negative number. However, I'm not sure what that number represent, nor am I sure I did this correctly.

        Thomas Thomassen β€” SketchUp Monkey & Coding addict
        List of my plugins and link to the CookieWare fund

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        • C Offline
          Chris Fullmer
          last edited by 23 May 2009, 21:34

          Perhaps the cross method is best. The cross method of 2 vectors will return a vector that is perpendicular to the plane they lie on. (this is using colors as defind by SketchUp) So if you do green.cross red, that returns the blue axis vector ([0,0,1]. But if you do red.cross green you get the negative blue axis vector ([0,0,-1). So by doing the cross vector on your vectors you can determine if the 2 angle_between's rotated the same direction. If they did, then both cross vector products will be positive or both negative. But if angle_between rotated a different way to find each angle, then the cross product will return one true and one false. Does that make sense?

          Chris

          Lately you've been tan, suspicious for the winter.
          All my Plugins I've written

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          • T Offline
            thomthom
            last edited by 23 May 2009, 21:44

            Yes. It makes sense.
            Though, I also need to reliably determine the direction of one vector against another. I wonder if getting the cross and checking if it's positive or negative is certain to determine the direction of the angle.

            Thomas Thomassen β€” SketchUp Monkey & Coding addict
            List of my plugins and link to the CookieWare fund

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            • B Offline
              BillW
              last edited by 24 May 2009, 21:07

              Thom

              Following on from Chris, I dont know if this code snippet from one of my tools helps

              
              def checkside(v1,v2)
                v3 = v1.cross(v2)
                return ((v3.z < 0) ? 1 ; -1)
              end
              
              # main body
              v1 = @pts[1].vector_to(@pts[2])
              @alignment = checkside(@stairdirvec,v1)
              
              
              

              It returns 1 or -1 depending on which side I need to draw. @stairdirvec is the primary direction which v1 is tested against.

              BillW

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              • F Offline
                fredo6
                last edited by 24 May 2009, 21:31

                @unknownuser said:

                You have to choose a Z direction (perpendicular to the plane of the two vectors, in order ot orient your angles.
                Otherwise it is normal that you get the same value (just imagine you look at your picture from the back!).

                Then you make a difference by the sign of (vec1 * vec2) % vecZ

                Fredo

                Just to make clearer what I said in an earlier post. Referring to the picture, you have 3 vectors: red, blue and black.

                If you wish to measure the 'oriented' angles between 'blue and black' and 'blue and red', you must decide on a reference rotation direction (in plane geometry, we would count in the trigonometric sense, or anti-clockwise).

                The reference direction is what you want, but is perpendicular to the other vectors. So, for instance, if you are fine with the angle returned by vec_black.angle_between(vec_blue), then the reference direction would be

                
                vec_rotation_ref = vec_black * vec_blue
                
                

                Now, for the red vector, you compute vec_black * vec_red
                and then compare its orientation with your reference rotation vector, by making the scalar product (which is negative if the vectors have opposite directions, and positive otherwise).

                
                angle_red = vec_black.angle_between(vec_red)
                if vec_black * vec_red) % vec_rotation_ref < 0
                   angle_red = 2 * Math;PI - angle_red
                end
                
                

                Note that if you work in the horizontal plane, the you can take Z_AXIS as your reference rotation vector (and then Bill'sformula works).

                Fredo

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                • T Offline
                  thomthom
                  last edited by 25 May 2009, 06:31

                  Thanks for clarifying that Fredo. I had temporary used a fixed [0,0,1] vector for references. (The plugin I work on works completely planar.)

                  @unknownuser said:

                  you must decide on a reference rotation direction (in plane geometry, we would count in the trigonometric sense, or anti-clockwise).

                  By a 50/50% chance I'd chosen counter-clockwise. πŸ˜„

                  Thomas Thomassen β€” SketchUp Monkey & Coding addict
                  List of my plugins and link to the CookieWare fund

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                  • Didier BurD Offline
                    Didier Bur
                    last edited by 25 May 2009, 11:17

                    Hi,
                    If this can help:

                    def angle2Pi(p1,p2)
                    	twoPI = 2.0*Math;;PI
                    	return (Math.atan2(p2.y-p1.y, p2.x-p1.x)+twoPI).modulo(twoPI)
                    end
                    

                    This returns the angle of a vector that starts at point p1 and ends at point p2, no matter wether p1 or p2 is the starting vertex. this is recommanded you use this only in 2D of course.
                    Regards,

                    DB

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                    • T Offline
                      thomthom
                      last edited by 2 Jul 2009, 19:41

                      @unknownuser said:

                      @unknownuser said:

                      You have to choose a Z direction (perpendicular to the plane of the two vectors, in order ot orient your angles.
                      Otherwise it is normal that you get the same value (just imagine you look at your picture from the back!).

                      Then you make a difference by the sign of (vec1 * vec2) % vecZ

                      Fredo

                      Just to make clearer what I said in an earlier post. Referring to the picture, you have 3 vectors: red, blue and black.

                      If you wish to measure the 'oriented' angles between 'blue and black' and 'blue and red', you must decide on a reference rotation direction (in plane geometry, we would count in the trigonometric sense, or anti-clockwise).

                      The reference direction is what you want, but is perpendicular to the other vectors. So, for instance, if you are fine with the angle returned by vec_black.angle_between(vec_blue), then the reference direction would be

                      
                      > vec_rotation_ref = vec_black * vec_blue
                      > 
                      

                      Now, for the red vector, you compute vec_black * vec_red
                      and then compare its orientation with your reference rotation vector, by making the scalar product (which is negative if the vectors have opposite directions, and positive otherwise).

                      
                      > angle_red = vec_black.angle_between(vec_red)
                      > if vec_black * vec_red) % vec_rotation_ref < 0
                      >    angle_red = 2 * Math;PI - angle_red
                      > end
                      > 
                      

                      Note that if you work in the horizontal plane, the you can take Z_AXIS as your reference rotation vector (and then Bill'sformula works).

                      Fredo

                      Ok, I've been trying to get this to work no-planar. But I'm having problems with the reference vector - because I don't have both the vectors to compare against at that point of the code.
                      I only have a base vector - that one that I compare against.

                      I've been trying to take the cross of the base vector (black) and the vector I compare against (red/blue), but it seem to be 50/50 chance that the cross vector points in opposite directions. Not sure how to orient it predictably....

                      Thomas Thomassen β€” SketchUp Monkey & Coding addict
                      List of my plugins and link to the CookieWare fund

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                      • B Offline
                        bentleykfrog
                        last edited by 3 Mar 2011, 13:49

                        Sorry for digging up another old topic, here's my not-so-rough guess at a long way around.

                        angle1 = black_vector.angle_between red_vector
                        vector_cross = black_vector.cross red_vector
                        vector_90 = black_vector.cross vector_cross
                        angle2 = vector_90.angle_between red_vector
                        angle1 = (Math;;PI-angle1) + Math;;PI if angle2 >= (Math;;PI/2)
                        
                        
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                        • B Offline
                          bentleykfrog
                          last edited by 3 Mar 2011, 13:55

                          Also, as a bit of a bodge to fix the 50/50 direction problem

                          vector_90 = Geom;;Vector3d.new(vector_90[0].abs,vector_90[1].abs,vector_90[2].abs)
                          
                          

                          Its probably not efficient, or even tested

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                          • B Offline
                            bentleykfrog
                            last edited by 21 Sept 2011, 10:04

                            I've been working on this problem quite alot lately, and I've realised the code I posted is wildly incorrect, as you say ThomThom:
                            @thomthom said:

                            it seem to be 50/50 chance that the cross vector points in opposite directions.

                            so we should probably compare the cross vector against something relatively static, like one of the model axes?

                            @unknownuser said:

                            Note that if you work in the horizontal plane, the you can take Z_AXIS as your reference rotation vector (and then Bill'sformula works).

                            could this work if we reverse the cross vector based on its angle to the Z_AXIS (ie. greater than 90 degrees then reverse cross vector).

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                            • B Offline
                              bentleykfrog
                              last edited by 21 Sept 2011, 16:44

                              @bentleykfrog said:

                              I've been working on this problem quite alot lately

                              πŸ˜„ I've finally got my 2d manifold detection working (albeit quite slowly as I have to calculate an infinite line [planar normal of an edge] intersecting a complex polygon [face] for each edge to determine the side of the edge its associated face is on). Anyway I thought I'd post the code here for some feedback and optimization advice. Here's the code snippet: feel free to chop/change/reuse if you like.

                              		def intersect_line_line_segment_2d(line,segment)
                              			x1	= line[0].x
                              			y1	= line[0].y
                              			x2	= line[1].x
                              			y2	= line[1].y
                              			x3	= segment[0].x
                              			y3	= segment[0].y
                              			x4	= segment[1].x
                              			y4	= segment[1].y
                              			
                              			u_line_n = ((x4 - x3)*(y1 - y3)) - ((y4 - y3)*(x1 - x3))	#line equation numerator
                              			denom	 = ((y4 - y3)*(x2 - x1)) - ((x4 - x3)*(y2 - y1))	#line  & segment equation denominator
                              			
                              			u_segment_n	= ((x2 - x1)*(y1 - y3)) - ((y2 - y1)*(x1 - x3))	#segmnet equation numerator
                              			
                              			if denom == 0
                              				#line and segment are parallel
                              				return false
                              			end #if
                              			
                              			u_segment = u_segment_n.quo(denom)
                              			
                              			if u_segment >= 0 || u_segment <=1
                              				#return [x1 + (u_segment*(x2-x1)),y1 + (u_segment*(y2-y1)),1]	#use to return the point of intersection
                              				u_line = u_line_n.quo(denom)									#use to return a relative distance value for ordering
                              				return u_line													#intersections on a complex polygon
                              			else
                              				#intersection is outside the line segment
                              				return false
                              			end
                              		end #def
                              		
                              		def find_manifold_face(origin_face_id,fold_edge_id,possible_face_ids,check_orientation=false,correct_orientation=false)		
                              			origin_face		= @@face_objects[origin_face_id]
                              			origin_edges	= @@faces_to_edges[origin_face_id]
                              			manifold_face	= false
                              			
                              			#	PT1; ORIGIN FACE->FOLD EDGE ORIENTATION
                              			#	we need to find on which side of the edge the face is, and then
                              			#	determine the direction of rotation. This is more difficult than
                              			#	it appears. The most error-free way to do it is to create a line
                              			#	that represents the planar normal for the edge (ie perpendicular
                              			#	to the fold edge and on the plane of the origin face) and find the
                              			#	line segments that intersect with the face using an Intersect Segment
                              			#	with Polygon algorithm. [see; http://softsurfer.com/Archive/algorithm_0111/algorithm_0111.htm]
                              			#	A COUPLE OF NOTES FIRST;
                              			# 1;We only need a 2d coordinate system for this so we can use the UVHelper
                              			#	to generate this and hopefully make the code more efficient
                              			# 2;We only need to find the first intersected line segment that shares
                              			#	one of its points with the fold edge
                              			fold_verts 		= @@edges_to_verts[fold_edge_id]					#construct points on the fold edge that will help with
                              			fold_arr		= fold_verts.values									#orientation; pt1; start, pt2; middle, pt3; end
                              			fold_pt1		= fold_arr[0].position
                              			fold_pt3		= fold_arr[1].position
                              			fold_pt2		= fold_pt1 + Geom;;Vector3d.new((fold_pt3.x-fold_pt1.x).quo(2),(fold_pt3.y-fold_pt1.y).quo(2),(fold_pt3.z-fold_pt1.z).quo(2))
                              			fold_vec		= fold_pt1.vector_to fold_pt3
                              			trans 			= Geom;;Transformation.rotation fold_pt2, origin_face.normal, -90.degrees
                              			o_vec1 			= fold_vec.transform trans
                              			
                              			origin_uvhelp 	= origin_face.get_UVHelper true, false, @@tw		#UVHelper can give us 2d coordinates for a 3d face ;)
                              			fold_uv_pt1		= origin_uvhelp.get_front_UVQ(fold_pt1)				#construct the corresponding uv points that are uv
                              			fold_uv_pt2		= origin_uvhelp.get_front_UVQ(fold_pt2)				#representations of the 3d coordinates
                              			fold_uv_pt3		= origin_uvhelp.get_front_UVQ(fold_pt3)
                              			fold_uv_vec		= fold_uv_pt1.vector_to fold_uv_pt3
                              			
                              			trans_uv_vec	= Geom;;Vector3d.new(fold_uv_vec[1],-fold_uv_vec[0],1)		#construct a fold edge normal line to
                              			trans_uv_pt		= fold_uv_pt2 + trans_uv_vec								#calculate the line segments of intersection
                              			trans_uv_line	= [fold_uv_pt2, trans_uv_pt]
                              			
                              			intersection_array = Array[0]
                              			origin_edges.each {|edgeID|
                              				next if fold_edge_id == edgeID
                              				edge_uv_pt1	= origin_uvhelp.get_front_UVQ(@@edge_objects[edgeID].start.position)
                              				edge_uv_pt2 = origin_uvhelp.get_front_UVQ(@@edge_objects[edgeID].end.position)
                              				edge_uv_segment = [edge_uv_pt1, edge_uv_pt2]
                              				
                              				intersection_u = self.intersect_line_line_segment_2d(trans_uv_line,edge_uv_segment)
                              				next if !intersection_u
                              				intersection_array << intersection_u
                              			}
                              			if intersection_array.length <= 1
                              				msg = "Critical Error; Normalize Toolkit encountered an illegal face (a face with only two vertices).\nYour model probably has errors?"
                              				msg += "To check, select the menu item 'Window' -> Model Info, then select 'Statictics' and click on 'Fix Problems'."
                              				self.alert_error(msg,true)
                              				Sketchup.send_action CMD_SELECT
                              				return false			
                              			end #if
                              			
                              			intersection_array.sort!									#ok lets find if the vector is pointing the right way
                              			reverse = (intersection_array.index(0) % 2) ? 1 ; -1
                              			o_vec1.reverse! if reverse == -1
                              			o_pt1 = fold_pt2 + o_vec1
                              			o_vec2 	= origin_face.normal								#make the origin face's normal an orientation vector
                              																		#we need two vectors at right angles to get around the
                              																		#angle_between not greater than 180 degrees problem.
                              			smallest_angle 	= 360.degrees
                              			possible_face_ids.each {|faceID|
                              				next if !@@faces_to_verts.has_key?(faceID)
                              				next if faceID == origin_face_id
                              				
                              				#logically, the p_vec1 should be found by rotating the fold_vec in the opposite direction
                              				#as o_vec1 was. The only issue here is that if the normal is reversed, we wont get a correctly
                              				#facing vector. Fortunately, we can determine this by comparing the clockwise angle from o_vec1
                              				#to p_vec1 and from o_vec1 to @@face_objects[faceID].normal.
                              				#If o_vec1 to p_vec1 is smaller than o_vec1 to @@face_objects[faceID].normal, we've got a reversed
                              				#normal!! cool
                              				trans 			= Geom;;Transformation.rotation fold_pt2, @@face_objects[faceID].normal, reverse * 90.degrees
                              				p_vec1 			= fold_vec.transform trans
                              				
                              				t_ang1a			= o_vec1.angle_between @@face_objects[faceID].normal
                              				t_ang1b			= o_vec2.angle_between @@face_objects[faceID].normal
                              				t_ang2a			= o_vec1.angle_between p_vec1
                              				t_ang2b			= o_vec2.angle_between p_vec1
                              				
                              				t_ang1 = (t_ang1b <= 90.degrees) ? t_ang1a ; 180.degrees + (180.degrees - t_ang1a)
                              				t_ang2 = (t_ang2b <= 90.degrees) ? t_ang2a ; 180.degrees + (180.degrees - t_ang2a)
                              				
                              				#another problem here is that the difference between t_ang1 & t_ang2 should be roughly plus or minus 90 degrees
                              				#if its greater, then the possible face is on such an obtuse angle and reversed that its normal is closer to
                              				#o_vec1 than p_vec1 is
                              				p_vec1.reverse! if ((t_ang1 > t_ang2) || ((t_ang2 - t_ang1) > 180.degrees))
                              				
                              				o_ang1 = o_vec1.angle_between p_vec1
                              				o_ang2 = o_vec2.angle_between p_vec1
                              				
                              				manifold_angle = (o_ang2 <= 90.degrees) ? o_ang1 ; 180.degrees + (180.degrees - o_ang1)
                              
                              				if manifold_angle < smallest_angle
                              					smallest_angle = manifold_angle
                              					manifold_face = @@face_objects[faceID]
                              				end
                              			}
                              			if !manifold_face
                              				return false
                              			end
                              			
                              			if check_orientation
                              				direction = self.get_rotation_direction(fold_vec,fold_pt2,origin_face.normal,o_pt1)				#work out whether the vector is pointing in the right direction
                              				trans 	= Geom;;Transformation.rotation fold_pt2, fold_vec, (smallest_angle * direction)		#rotate the origin normal so its aligned with
                              				m_normal 	= o_vec2.transform trans															#the manifold's normal. This should give a vector
                              				m_ang1		= m_normal.angle_between manifold_face.normal										#that angles 180 degrees from the manifold's normal
                              				oriented = (m_ang1 > 90.degrees) ? true ; false													#if its less than 90 degrees, reverse the face.
                              				return Hash[
                              					"manifold_face" => manifold_face,
                              					"oriented"	=> oriented
                              				]
                              			end #if
                              			
                              			return manifold_face
                              		end #def
                              
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                              • B Offline
                                bentleykfrog
                                last edited by 21 Sept 2011, 19:14

                                just for context, attached is the wip with a few modifications to the previous post to reduce the load significantly if we're dealing with convex polygons.


                                normalize toolkit work in progress

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                                • M Offline
                                  mac1
                                  last edited by 23 Sept 2011, 15:55

                                  See if any ideas here help. Tried to find arctan2 for three 3d. More search probably required
                                  http://www.euclideanspace.com/maths/algebra/vectors/angleBetween/index.htm

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                                  • Dan RathbunD Offline
                                    Dan Rathbun
                                    last edited by 23 Sept 2011, 22:20

                                    atan2() is one of the methods in the standard Ruby Math module.

                                    Somewhere TIG posted an example method of using it with Sketchup API units.

                                    I'm not here much anymore.

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                                    • B Offline
                                      bentleykfrog
                                      last edited by 24 Sept 2011, 04:10

                                      wow, major oversight! I should probably be using edge.reversed_in? to reliably find the edge normal direction relative to the face.

                                      Just to double-check my logic: on outer loops edge.reversed_in? will return true if the start and end vertex of the edge is running clockwise (if your looking against the normal of the face [the negative face normal vector is the vector for determining clockwise or anti-clockwise]). On inner loops (face.loops - face.outer_loop) edge.reversed_in will return true if the start and end vertex of the edge is running counter-clockwise?

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                                      • M Offline
                                        mac1
                                        last edited by 24 Sept 2011, 04:33

                                        Once one determines the angle value the inverse trig functions calculate the principal value. Therefore to determine the actual angle logic must be use either in the method or in the program its self to determine the correct quadrant. Give one can get the cos from the dot product, sine from the cross and even tangent from tan( theta) = |V1xV2|/ (V1 dot V2) then it is possible to establish the quadrant??

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                                        • T Offline
                                          thomthom
                                          last edited by 26 Sept 2011, 07:34

                                          @bentleykfrog said:

                                          wow, major oversight! I should probably be using edge.reversed_in? to reliably find the edge normal direction relative to the face.

                                          Just to double-check my logic: on outer loops edge.reversed_in? will return true if the start and end vertex of the edge is running clockwise (if your looking against the normal of the face [the negative face normal vector is the vector for determining clockwise or anti-clockwise]). On inner loops (face.loops - face.outer_loop) edge.reversed_in will return true if the start and end vertex of the edge is running counter-clockwise?

                                          Aye. Loop and EdgeUse objects can be very useful.

                                          Thomas Thomassen β€” SketchUp Monkey & Coding addict
                                          List of my plugins and link to the CookieWare fund

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