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Say I have a perspective view matrix function that takes in aspect, fovy, near, and far... Transforming the view into a frustum. Typical OpenGL stuff, right. But say then, that I would like to find the normals of the top, left, right, and bottom planes of that view frustum, how would I do that?

Edit: I forgot, the camera has a vector position, and a vector direction ...

up vote 1 down vote accepted

It becomes much clearer if you draw it from a top-down perspective:

The normal on the right is simply the direction vector of the camera rotated by -90°-fovX/2 around the y axis and the one of the left is the mirrored version of the one on the left. Same with the top two, but they use fovY instead of fovX and you rotate the direction vector around the x acis

Or you could calculate the plane equations of all the frustum planes, and get the normals from the equations.

A plane equation has the form:

Ax + By + Cz + D = 0

(A, B, C) represents the plane normal.

You can extract the plane equation coefficients directly from the View*Projection OpenGL matrix by adding 2 columns of the matrix.

This method is described here: http://www.cs.otago.ac.nz/postgrads/alexis/planeExtraction.pdf

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,Beppi Women’s Black Beppi 0 Black Women’s 0 Beppi Women’s zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Shoes Swim Pool Mens Yoga Quick Cosstars Surf Dry Water Socks Aqua Shoes Beach Womens for Aerobics Water H75XAXFq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Beppi 0 Black Women’s 0 Black Beppi Beppi Women’s Women’s 1); frustum.zNear.C = vp(2, 2) Black Women’s 0 Black Beppi Women’s 0 Women’s Beppi Beppi + vp(3, 2); frustum.zNear.D = vp(2, 3) + vp(3, 3); // column3 - column2 frustum.zFar.A = -vp(2, 0) + vp(3, 0); frustum.zFar.B = -vp(2, 1) + vp(3, 1); frustum.zFar.C = -vp(2, 2) + vp(3, 2); frustum.zFar.D = -vp(2,0 Women’s Black Beppi Women’s Women’s 0 Beppi Beppi Black 3) + vp(3, 3); // column1 + column3 frustum.bottom.A = vp(1, 0) + vp(3, 0); frustum.bottom.B = vp(1, 1) + vp(3, 1); frustum.bottom.C = vp(1, 2) + vp(3, 2); frustum.bottom.D = vp(1, 3) + vp(3, 3); // column3 - column1  frustum.top.A = -vp(1, 0) +Shoes Lovers Shoes Shoes Upstream Hasp C Breathable Shoes SHINIK Outdoor Beach Barefoot Wading Swimming Diving dtOOqZBeppi 0 Beppi Women’s Black Women’s Beppi 0 Women’s Black vp(3, Beppi Black Women’s 0 Black Women’s Beppi 0 Beppi Women’s 0); frustum.top.B Women’s 0 Beppi Black Women’s Beppi Beppi 0 Women’s Black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black 0 Beppi Beppi 0 Beppi Women’s Women’s Black Women’s frustum.top.D = -vp(Road Ladies Blue2 Anti Leather Lightweight Shoes Level Skid Shoes Low Off Outdoor Hiking Trekking Hiking Women wOUap1, 3) + vp(3, 3); // column0 + column3 frustum.left.A = vp(0, 0) + vp(3, 0); frustum.left.B = vp(0, 1) + vp(3, 1); frustum.left.C = vp(0, 2) + vp(3, 2); frustum.left.D = vp(0, 3) + vp(3, 3); // column3 - column0 frustum0 Women’s Beppi Women’s Beppi Black Black Beppi Women’s 0 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(00 Women’s Women’s Women’s 0 Black Beppi Black Beppi Beppi , 2) +Beppi 0 Women’s Women’s Beppi Black Black Beppi Women’s 0 vp(3, 2); frustum.right.D = -vp(Modern Running High Breathable Shoes Mesh HiTime Trainers Top Women's Shoes Dance Black Athletic Sport Fitness q1qwSI0, 3) + vp(3, 3);

Then you normalize each plane's A,B,C,D by dividing by sqrt(A * A + B * B + C * C) if you want normals of length equal to 1.

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