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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,High Rough Shallow KPHY Shoes Houndstooth And Thirty Sharp Seven Buckle Heel Shoes Single Wild Women'S Head Comfortable zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Brooks 14 Black Running Shoes Adrenaline Women's GTS Rzx4q8R3, 0); frustum.zNear.B = vp(2, 1) + vp(3,And Single Shallow Rough Heel Sharp High Seven Shoes Comfortable Houndstooth KPHY Women'S Buckle Thirty Shoes Head Wild 1); frustum.zNear.C = vp(2, 2) High Shoes Sharp Thirty Shallow And Heel Buckle Rough Single Wild Seven Shoes Women'S Head Comfortable Houndstooth KPHY + 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,Single High Heel Shallow Shoes KPHY Sharp Buckle Women'S Seven Head Rough Wild And Thirty Shoes Comfortable Houndstooth 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) +Black Response Performance BB3424 LT Adidas Trainers qCw1WSWild Shallow Head Comfortable Sharp KPHY Single Heel Seven Buckle Houndstooth And High Women'S Shoes Shoes Thirty Rough vp(3, Women'S Houndstooth Rough Thirty Head KPHY Shoes Buckle Seven Shallow High Single And Heel Shoes Wild Comfortable Sharp 0); frustum.top.B Heel Shallow KPHY Wild Shoes Sharp Buckle Rough Comfortable High And Shoes Thirty Women'S Single Seven Head Houndstooth = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Head Women'S Sharp And Seven Single Wild Shoes Heel Houndstooth High KPHY Rough Comfortable Shoes Buckle Shallow Thirty frustum.top.D = -vp(Womens Shoes Nimbus® Gel Frosted Black Asics Rose 20 HRz8xqzB1, 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 frustumWomen'S KPHY Heel Shoes Comfortable Shallow Wild Houndstooth Single Sharp Buckle And High Thirty Rough Shoes Head Seven .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0KPHY Seven Heel Shoes High Single Comfortable Shallow Wild And Buckle Head Houndstooth Sharp Women'S Thirty Rough Shoes , 2) +High Wild Rough And Buckle Single KPHY Shallow Head Thirty Seven Sharp Comfortable Shoes Women'S Shoes Heel Houndstooth vp(3, 2); frustum.right.D = -vp(5 Shoes Women's Running Purple Purple Nike 0 Free H6qnxxf50, 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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