#18898 - 05/04/06 07:19 AM
3D views, perspective, axonometry, similarity
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Milan
Member
Registered: 12/12/01
Posts: 2240
Loc: Brisbane, Queensland, Australi...
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A) Introduction
After months of research and work I have finally published a group of the three principal 'collineation transformation' macros in the Macro section, User Files at the Home Website of General Cadd Pro.
Collineation and Affinity are important TOOLS for the work on '3D view' drawings.
You can download those free macros from here, RightClick, SaveTargetAs.......
1) For Perspective, photography use and optics you download the 'General Collineation Transformation':
http://www.generalcadd.com/gxm/CollinearTransformation4-Ver01.GXM
2) For Axonometry, various tasks in constructive geometry and your 'User Coordinate System' (UCS) you use the 'Affinity Transformation':
http://www.generalcadd.com/gxm/AFFINITY3-Ver01.GXM
3) For Similarity, Translation, scaled or not, Identity, with an inbuilt option for the Least Squares adjustment you use the 'Linear Conformal Transformation', which was published earlier in the Surveyor's section of this Forum as the famous 'Helmert Transformation':
http://www.generalcadd.com/gxm/HM-HELMERT-01.GXM
In all the three macros you select first the objects which are to be transformed, than you draw the 'transit' lines connecting the pairs of the 'identical points'.
You set your Current Layer first - this will be the destination layer for all the transformed objects.
Note, the layers 1000, 1001, 1002 will be deleted !
B) Examples
1) For 'General Collineation' four transit lines are needed:
a) Mobius Mesh - the basics
Known also as the 'Projective Transformation', 'Eight Parameters Collinear Transformation'.
The 'collinear' means it 'shares the same lines' - the rays of light are a good example.
It preserves the 'Cross Ratio' following the Papus theorem.
More simply we can say it preserves the HARMONY.
Four transit lines are needed:
b) The use in 'two vanishing points' perspective, known also as the 'Corner Perspective', popular for architectural views:
c) The use in 'three vanishing points' perspective, used also with photography:
d) The use in photogrammetry - no field measurement needed, just take a picture:
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2) For AFFINITY Transformation three transit lines are needed:
a) For use in Axonometry, the drawing views for technical drawings.
Known in my part of the world as the 3000 years old 'Chinese perspective', and yes it is a perspective from infinity.
Known also as six parameters collinear transformation.
It preserves PARALLELIZM.
b) For the transformation to the 'User Coordinate System' (UCS) from the General Cadd Pro X/Y native CCW (counterclockwise) system and back.
Affinity (Orig. Latin: affinis 'connected with, related') plays important role between CW and CCW Cartezian (orthonormal) systems and also handles the 'elliptical' (non orthonormal) coordinate systems, that is the transformation between them.
Such transformations are reversing (reversible).
Note, the GREEN and PINK ordinates must be of the same length - and they are !!
Note, my invention of 'UCS Wheel' and the transit lines arrangement.
First, there is a double NP click on marked Origin Point.
Second and third transit lines are connecting the tips of the arrows in the appropriate order.
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3) For 'Linear Conformal Transformation'
Similarity requires two transit lines, Translation and Identity only one transit line.
This is covered by my earlier macro called the 'Helmert Transformation' and discussed in the Surveyor's corner.
http://www.generalcadd.com/ubb/ultimatebb.php/ubb/get_topic/f/24/t/000073.html
Adjustment by Least Squares option with statistics is available from two or more transit lines.
It is 'four parameters' transformation.
It is CONFORMAL, that is it preserves ANGLES.
_________________________
Milan
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#18899 - 05/04/06 12:47 PM
Re: 3D views, perspective, axonometry, similarity
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Noel H. Browning
Member
Registered: 12/11/01
Posts: 862
Loc: Glendale, CA
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Milan,
Wow!
Noel 
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#18900 - 05/04/06 01:03 PM
Re: 3D views, perspective, axonometry, similarity
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GCP Support
Member
Registered: 12/17/01
Posts: 3345
Loc: Cherry Valley, N. Y.
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Pretty Awesome! 
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#18901 - 05/04/06 05:35 PM
Re: 3D views, perspective, axonometry, similarity
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Bruce L
Member
Registered: 02/05/02
Posts: 822
Loc: Minneapolis, Minnesota
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Milan;
WOW!
Bruce
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#18902 - 05/04/06 09:43 PM
Re: 3D views, perspective, axonometry, similarity
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Sean
Member
Registered: 01/06/02
Posts: 1049
Loc: Whistler, Canada
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Stunning accomplishment Milan !!!
I look forward to trying it.
Sean
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#18903 - 05/05/06 06:17 AM
Re: 3D views, perspective, axonometry, similarity
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Vincent
Member
Registered: 06/25/02
Posts: 505
Loc: Newcastle, Australia
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WOW! Milan
Vincent 
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#18904 - 05/05/06 03:11 PM
Re: 3D views, perspective, axonometry, similarity
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Dondy2
Member
Registered: 03/29/02
Posts: 1404
Loc: Edmonton, Canada
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ECHO, ECHo, ECho, Echo! ! !
_________________________
Learn something Of VALUE, Every Day.
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#18905 - 05/05/06 10:31 PM
Re: 3D views, perspective, axonometry, similarity
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Milan
Member
Registered: 12/12/01
Posts: 2240
Loc: Brisbane, Queensland, Australi...
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Guys, thank you for your support !
I have received a good suggestion for an easy 'Esc and start all over' from Vincent, so Versions 02 will be published soon for the Collineation and Affinity.
Anybody else has a suggestion ?
Advisers are and would be listed in those macros....:
; ; GENERAL COLLINEAR TRANSFORMATION 4 - Ver.02 - The 'General Perspective' Tool
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; Author: Milan Anthony Vlasak, Eng.(Prague)
; May 2006, Brisbane, Queensland, Australia
; This Macro is Version 02 and it is free for use with a copy of General Cadd Pro
;
; Advisers:
; Ass.Prof.RNDr.Maria Kmetova,PhD., University of Konstantina Filozofa, Slovakia - Bezier Curve approximation in collineation
; Vincent Ferrara, Newcastle, Australia, Member of General Cadd Pro Forum - [Esc] easy to start all over
;
; Disclaimer:
; You assume total responsibility for using this macro
;
_________________________
Milan
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