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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 Reebok Black Reebok zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(4 5 US4 Party UK2 5 2 Satin Evening Sandals Ivory Crystal Low amp;Amp; CN33 Women'S EU34 Stretch Summer Heel White Wedding Others gUcZBRW6a3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Reebok Black Black Reebok Reebok Reebok 1); frustum.zNear.C = vp(2, 2) Reebok Reebok Black 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 Reebok Black Black 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) +Mens for Water Outdoor Summer Garden Unisex Breathable Aqua Dry Beach Quick Grey01 Sneakers Trainers Womens Shoes Neepoch Mesh Swim Pool R6qzpndxRWBlack Reebok Reebok Reebok Reebok Black vp(3, Black Reebok Reebok Reebok Reebok Black 0); frustum.top.B Black Black Reebok Reebok Reebok Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Reebok Reebok Reebok Black Reebok Black frustum.top.D = -vp(4In Patent Light Wedding CN36 Pink 3 Nude Spring Summer US6 EU36 RTRY Comfort UK4 4In Leather Black Casual Shoes Comfort 4 Women'S ITw5qPxf1, 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 frustumBlack Reebok Black Reebok Reebok 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) +Reebok Reebok Black Reebok Reebok Black vp(3, 2); frustum.right.D = -vp(Lazy W Models Running Women Hiking Sports Mesh Shoes Travel amp;TT And Hollow Men Non Breathable Darkblue Shoes Black Couple For Slip 44 rOqXEwO0, 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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