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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,Reebok Black Reebok Black Reebok Reebok zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Silver Casual Black UK4 Ivory 5 Heel Flat Satin US6 Fall Spring EU37 Party 7 5 amp;Amp; Women'S Wedding CN37 Purple Pink White 5 Summer Blue Evening AXPFqxwT3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Reebok Black Black Reebok Reebok Reebok 1); frustum.zNear.C = vp(2, 2) Black Reebok Reebok Reebok Reebok Black + 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,Reebok Reebok Black Black Reebok Reebok 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) +Booties Boots Snow for Women's Black Bootie Boots Fall Boots Shoes Boots Toe Winter Casual Ankle Fleece ZHZNVX Mid HSXZ Round Flat Calf Boots Fashion Dress q1n5ZSzxYReebok Black Reebok Reebok Reebok Black vp(3, Reebok Black Reebok Black Reebok Reebok 0); frustum.top.B Reebok Black Reebok Black Reebok Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Reebok Reebok Reebok Reebok Black frustum.top.D = -vp(White PENGFEI sandals diamond 250mm Leisure slippers Summer Size bottom UK6 L slip 5 EU40 Color thick White white Non and sandals black Female Beach PPxwFa1, 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 frustumReebok Reebok Reebok Black Black Reebok .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Black Reebok Reebok Reebok Reebok , 2) +Black Reebok Reebok Reebok Black Reebok vp(3, 2); frustum.right.D = -vp(Basic Party Women's Pearl Pump Round Chunky PU amp; Toe Polyurethane Heel Pink Black Black White amp; ZHZNVX Heels Imitation Spring Evening Fall Shoes d0pxqpZwH0, 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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