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We know that in Oblique Parallel Projection Point (x,y,z) is projected to position (x_p,y_p) on the view plane.Projector (oblique) from (x,y,z) to (x_p,y_p) makes an angle alpha. with the line (L) on the projection plane that joins (x_p,y_p) and (x,y). Line L is at an angle phi with the horizontal direction in the projection plane.See this image1: enter image description here

And in Oblique Parallel Projection Angles, distances, and parallel lines in the plane are projected accurately.For example see below image2:enter image description here

My question is where is the angle alpha in image2, I mean I see the angle phi on the image , so where is alpha in that image to understand better?I want to see 12 edges of original image projected to view plane with projector and angle alpha,phi levelling.

N. B:1 -- I am following Hearn and Baker book which screenshot like this.

N. B. -- I want to understand just intuition in easy way rather than details.

S. M.
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  • Alpha cannot be depicted on Image2, because it goes out of the plane. – Theraot Dec 06 '21 at 19:05
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    I’m voting to close this question because it is a cross post of https://engineering.stackexchange.com/questions/48585/how-to-visualize-angle-of-projection-in-oblique-parallel-projection – Theraot Dec 06 '21 at 19:06
  • @Theraot could you provide the only the image "12 edges of original image projected to view plane with projector and angle alpha,phi levelling." – S. M. Dec 06 '21 at 19:10
  • I'm convinced the best way to visualize this would be with 3D graphics. Which is entirely odd because we would be using a projection to understand another one. I'll try to find if somebody has done it, I really don't want to program it. – Theraot Dec 06 '21 at 19:20
  • @Theraot I just want only the image. – S. M. Dec 06 '21 at 19:27
  • Yes, but you have an image. I'm not sure the one you want will make the difference. Anyway, if I understand correctly, you want one like the one on Wikipedia (but with the angles labelled): https://en.wikipedia.org/wiki/Oblique_projection#/media/File:Axonometric_projection.svg Let alone all the noise, how is the plane positioned in space there? (Orbiting around it would make it easy to grasp) - This is the best I have found so far: https://www.youtube.com/watch?v=xWOMcGkHUIc - Keep in mind that alpha is between the segment that goes from a point to its projection, and the projection plane. – Theraot Dec 06 '21 at 19:33
  • @Theraot could you label the image of wiki with angle alpha and phi? – S. M. Dec 06 '21 at 19:38
  • I have the problem I described above. I don't know how the plane is positioned. I'll keep looking. – Theraot Dec 06 '21 at 19:46
  • I hope this does it for you: https://i.stack.imgur.com/MFMO5.png I created that with Sketchup and Gimp. – Theraot Dec 06 '21 at 20:05
  • But I have one request, could you level all places where alpha and phi esixts? – S. M. Dec 06 '21 at 20:12
  • Blue is alpha, green is phi; different views: https://i.stack.imgur.com/uXQaC.png, https://i.stack.imgur.com/1cVvD.png, https://i.stack.imgur.com/jxMse.png, https://i.stack.imgur.com/SFaUb.png, https://i.stack.imgur.com/AV5Bs.png, https://i.stack.imgur.com/tzsR1.png, https://i.stack.imgur.com/oUKR7.png – Theraot Dec 06 '21 at 20:36
  • @Theraot Wow, Could you insert your comments in your answer I will accept it. – S. M. Dec 06 '21 at 20:41
  • Cross-posted: https://gamedev.stackexchange.com/q/198224/82314, https://engineering.stackexchange.com/q/48585/7678. Please do not post the same question on multiple sites. – D.W. Dec 30 '21 at 20:05

1 Answers1

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On OP request, I'm posting the images I produced as answer.

These were made with Sketchup. They show a cube a plane where the cube is projected in an oblique projection. The blue sectors represent the angle alpha, and green sectors represent the angle phi. Observe that the angle phi exists entirely in the projection plane, while alpha does not. Instead alpha is the angle between the projection plane and the segment that goes from a point to its projection. As a consequence it is impossible to depict alpha on the projection plane, since it goes out of it. Furthermore, depicting alpha requires knowing the relative position of the object and the projection plane.

These images have perspective. It is odd to me that I'm using a projection to visualize another. However, I believe this is the best way to gain an intuition of it (actually I believe being able to orbit at will is better, but sans that here are multiple views).

I believe these are Cabinet, unless I'm confusing things.

enter image description here

enter image description here

enter image description here

enter image description here

enter image description here

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enter image description here

Animation:

enter image description here

Theraot
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  • on 3rd image only phi angle but why alpha is absent? – S. M. Dec 06 '21 at 21:17
  • @Ponting Alpha is on a plane you are looking on edge. Well, almost, due to the perspective, you can slightly see it: https://i.stack.imgur.com/tuDQl.png - Notice I only marked 4 of the 8 alpha, the other 4 are reduced to a line - But if I were using an orthographic projection, they would all be reduced to a line. By the same logic phi is not visible on the 6th picture. – Theraot Dec 06 '21 at 21:23
  • one thing tell projection of cube you take front face of original image is perpendicular parallel projection on projection plane? – S. M. Dec 06 '21 at 21:45
  • @Ponting Yes, I did project the closer face to the plane perpendicularly to it. Now I'm thinking I shouldn't have done that. I'll re do it (edit: I see, I made a cavalier projection, which is considered a type of oblique projection, but what we want in this case). – Theraot Dec 06 '21 at 22:07
  • in Cabinet also front face is also perpendicular to projected image. – S. M. Dec 07 '21 at 10:04
  • @Ponting Well, I'm projecting the same thing. However, it does not have to be perpendicular. – Theraot Dec 07 '21 at 10:09
  • your cabinet become oblique due to absence of perpendicular. – S. M. Dec 07 '21 at 10:12
  • @Ponting Let us continue this discussion in chat. – Theraot Dec 07 '21 at 10:22
  • please check my image with alpha position is right or not? https://drive.google.com/file/d/1a0ghThVkmhJb3z1w2pTqy5c1fzegmYMe/view?usp=drivesdk – S. M. Dec 07 '21 at 15:31
  • @Ponting I still think alpha cannot be depicted in the picture https://i.stack.imgur.com/waFgn.jpg. I don't know how to interpret what you did here https://drive.google.com/file/d/1a0ghThVkmhJb3z1w2pTqy5c1fzegmYMe/view – Theraot Dec 07 '21 at 15:46
  • how can visualize alpha and phi on this image https://i.stack.imgur.com/waFgn.jpg – S. M. Dec 07 '21 at 17:05
  • it possible to see visualize alpha and phi on this https://i.stack.imgur.com/waFgn.jpg.please reply, I am waiting for your reply. – S. M. Dec 07 '21 at 18:13
  • please help this question https://gamedev.stackexchange.com/questions/198583/is-diffuse-reflection-definition-failed-when-we-see-both-reflectiondiffuse-spec – S. M. Dec 29 '21 at 20:40