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Great_White

OpenGL Projection plane ?

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Great_White    148
hi all, I'm wondering what the projection plane is used in the OpenGL perspective transformation matrix. Are the vertices always projected to the near plane (i.e. z=-1).What if we change it to some arbitrary value?

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haegarr    7372
In fact there is no explicit projection plane needed.

The only planes are those limiting the viewing volume. Their requirement is that none of the 6 sides of the viewing volume is degenerated to a point (what the reason is that e.g. the near clipping plane must not be located at a distance of 0). As long as all 6 sides are 2 dimensional, the viewing volume can be transformed into the cube mentioned by Hodgman.

A projection plane doesn't hide anything (as opposed to clipping planes). And the precedence of a surface hit is only given by its closer distance to the origin on the projector line in comparison to other hits. So it plays no role whether a projection plane is on the near clipping plane, the far clipping plane, or in-between them (or even elsewhere).

Moreover, it isn't required that a projection plane is parallel to the near/far clipping planes. E.g. the oblique projections (although counting to the parallel projections but not to the perspective projection) have non-parallel projection planes w.r.t. the viewing volume.

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Great_White    148
Quote:
Original post by Hodgman
The vertices are transformed into clip space which you can visualise as a cube from [-1,-1,-1] to [1,1,1]


yes I know that, it is required since clipping can be done more efficiently in canonical view volume.

Quote:
Original post by haegarr
In fact there is no explicit projection plane needed.

The only planes are those limiting the viewing volume. Their requirement is that none of the 6 sides of the viewing volume is degenerated to a point (what the reason is that e.g. the near clipping plane must not be located at a distance of 0). As long as all 6 sides are 2 dimensional, the viewing volume can be transformed into the cube mentioned by Hodgman.

A projection plane doesn't hide anything (as opposed to clipping planes). And the precedence of a surface hit is only given by its closer distance to the origin on the projector line in comparison to other hits. So it plays no role whether a projection plane is on the near clipping plane, the far clipping plane, or in-between them (or even elsewhere).

Moreover, it isn't required that a projection plane is parallel to the near/far clipping planes. E.g. the oblique projections (although counting to the parallel projections but not to the perspective projection) have non-parallel projection planes w.r.t. the viewing volume.


hmm thats interesting I've recently read a chapter about the projection transformations in "Computer Graphics by Foley et. al", and it mentions a projection plane(which can be constucted by using view parameters, i.e. as in gluLookat() funtion ) for the projections.Besides it also shows a projection plane between near and far clipping planes. I'm a little bit confused :(

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haegarr    7372
Quote:
Original post by Great_White
hmm thats interesting I've recently read a chapter about the projection transformations in "Computer Graphics by Foley et. al", and it mentions a projection plane(which can be constucted by using view parameters, i.e. as in gluLookat() funtion ) for the projections.Besides it also shows a projection plane between near and far clipping planes. I'm a little bit confused :(
gluLookAt is a nice example, because its parameters are not sufficient to define a specific projection plane as you may expect! With the difference vector from "eye" to "center" you have a normal for planes, e.g. used directly for the near and far clipping planes. The normal alone isn't sufficient to express rolling, so there is the additional "up" vector. Now, adding the parameters of gluPerspective, you get the distances of the near and far clipping plane, and their sizes (due to field-of-view and aspect ratio). Then 4 sides of the viewing volume are implicitely given. That's all: The viewing volume is defined, but nothing like a distance or something alike for a projection plane!

Now think of perspective projection as a method that fires a straight ray from the camera's origin through the view volume (i.e. as ray-tracers work). This ray can be named a "projector". The ray hits a couple of object surfaces. Each hit in front of the near clipping plane or behind the far clipping plane is discarded. The remaining hits are sorted by distance (i.e. the depth), and all but the frontmost hit are discarded as well. The last hit is what is used to compute the shading for the pixel where the said ray passes through.

As you can see above there is no projection plane needed to compute the pixel values. If you really would do ray-tracing, you would have the nedd to compute the parameters of the ray. For this purpose you would define a plane, compute the pixel positions as defined by the view/window, and compute the rays passing through these positions. Even if you name this plane the projection plane, it does not play a role whether you use the near clipping plane, the far clipping plane, or any other (parallel) plane for this purpose. Each of those planes are equally sufficient for that purpose.

A "projection plane" can be convenient to specifiy the viewing volume if you want to define a size at a specific distance, i.e. independent of the near (or any other) clipping plane, or perhaps if you doesn't have front and back clipping planes at all. My good old ray-tracer did it this way. But hardware accelerated scanline 3D doesn't work this way. Even _if_ you have such a case, you can still pick any parallel plane (as long as you adapt its size correctly due to the field-of-view) to get the same result at the end.

That said, a projection plane is IMHO a nice instrument to imagine what happens, and is perhaps good for some intermediate computations, but there is not a single, specific plane for this purpose that must be used to yield in a specific result.

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Great_White    148
Quote:
Original post by haegarr
Quote:
Original post by Great_White
hmm thats interesting I've recently read a chapter about the projection transformations in "Computer Graphics by Foley et. al", and it mentions a projection plane(which can be constucted by using view parameters, i.e. as in gluLookat() funtion ) for the projections.Besides it also shows a projection plane between near and far clipping planes. I'm a little bit confused :(
gluLookAt is a nice example, because its parameters are not sufficient to define a specific projection plane as you may expect! With the difference vector from "eye" to "center" you have a normal for planes, e.g. used directly for the near and far clipping planes. The normal alone isn't sufficient to express rolling, so there is the additional "up" vector. Now, adding the parameters of gluPerspective, you get the distances of the near and far clipping plane, and their sizes (due to field-of-view and aspect ratio). Then 4 sides of the viewing volume are implicitely given. That's all: The viewing volume is defined, but nothing like a distance or something alike for a projection plane!

Now think of perspective projection as a method that fires a straight ray from the camera's origin through the view volume (i.e. as ray-tracers work). This ray can be named a "projector". The ray hits a couple of object surfaces. Each hit in front of the near clipping plane or behind the far clipping plane is discarded. The remaining hits are sorted by distance (i.e. the depth), and all but the frontmost hit are discarded as well. The last hit is what is used to compute the shading for the pixel where the said ray passes through.

As you can see above there is no projection plane needed to compute the pixel values. If you really would do ray-tracing, you would have the nedd to compute the parameters of the ray. For this purpose you would define a plane, compute the pixel positions as defined by the view/window, and compute the rays passing through these positions. Even if you name this plane the projection plane, it does not play a role whether you use the near clipping plane, the far clipping plane, or any other (parallel) plane for this purpose. Each of those planes are equally sufficient for that purpose.

A "projection plane" can be convenient to specifiy the viewing volume if you want to define a size at a specific distance, i.e. independent of the near (or any other) clipping plane, or perhaps if you doesn't have front and back clipping planes at all. My good old ray-tracer did it this way. But hardware accelerated scanline 3D doesn't work this way. Even _if_ you have such a case, you can still pick any parallel plane (as long as you adapt its size correctly due to the field-of-view) to get the same result at the end.

That said, a projection plane is IMHO a nice instrument to imagine what happens, and is perhaps good for some intermediate computations, but there is not a single, specific plane for this purpose that must be used to yield in a specific result.


thinking in terms of ray tracing terminolgy starting to make sense now.
Thanks.

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