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Hi there,
I've started learning 3D geometry and as an exercise, I made this C++
function that takes a point in 3D and projects it on a plane given its
normal, in easy english this would mean take any point anywhere and make
them all "fall" on an invisible surface.
Basically, in the images you see bellow, all points were randomly
generated with coordinates (x,y,z) within [-1,1]. With no
transformation, this gives a box filled with points. After applying the
geometric transformation, all points lies on the plane that the normal
points.
Graphically speaking, the images on the left were rendered with povray
3.6 on linux, I did not take rendering times, as it's pretty quick
(using spheres and cylinders). Images on the right were screenshots of
my OpenGL render (using points and lines). Both images were resized to
320x240 and the OpenGL images (right) had to go through a
brightness/contrast work to show the details.
In this scene, the 3 axes X, Y and Z are drawn with the lines in Red,
Green and Blue. The Grey line represents the normal of the imaginary
plane. The White dots represent the dots After transformation. Also,
the first image shows the scene looking at the origin, with a camera
position approx. like <10,10,10>, the normal(white line) = <1,1,1>. The
second image shows same origin with camera position approx. like
<0,2,10>. The last image shows same origin with camera position approx.
like <-10, 0, 10>.
PROOF:
First image shows an hexagon, a box looked from one of its corner looks
like an hexagon, but last image shows that the box was correctly reduced
to a simple plane in 3D space.
Hope you get it, hope you like it!
Simon
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Attachments:
Download 'point2plane_projection.gl2pov.1.jpg' (34 KB)
Download 'point2plane_projection.gl2pov.2.jpg' (23 KB)
Download 'point2plane_projection.gl2pov.3.jpg' (7 KB)
Preview of image 'point2plane_projection.gl2pov.1.jpg'
Preview of image 'point2plane_projection.gl2pov.2.jpg'
Preview of image 'point2plane_projection.gl2pov.3.jpg'
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