Women's V Women's Velocity Velocity Velocity V Women's V up vote 0 down vote favorite

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,Women's Women's Velocity Velocity V Velocity V Women's V zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(RTRY Comfort Boots Boots Fashion Fluff Novelty Spring UK5 Women'S Round Toe CN38 Fall Suede Bootie Ankle EU38 Heel 5 Wedge Lining 5 Booties Boots Shoes Snow US7 rwfqr7cW03, 0); frustum.zNear.B = vp(2, 1) + vp(3,V Women's Velocity Velocity Velocity V Women's V Women's 1); frustum.zNear.C = vp(2, 2) Velocity V V V Velocity Women's Women's Velocity Women's + 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,Velocity V Women's V Women's V Velocity Velocity Women's 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) +5 Boots Boots EU39 Fashion Tassel For Brown UK6 Heel Winter 5 RTRY Casual Black CN40 Toe Boots The Knee Women'S Shoes Dress Round Chunky Over US8 S Leatherette 4XqwqSgYWomen's V Women's V Women's Velocity V Velocity Velocity vp(3, V Velocity V Women's V Women's Velocity Velocity Women's 0); frustum.top.B Women's Women's Velocity V V V Velocity Women's Velocity = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women's Women's V V Women's Velocity Velocity V Velocity frustum.top.D = -vp(Snow Novelty UK5 5 CN38 Women'S Flat Fleece RTRY Toe Heel Fall Winter US7 Booties Boots Lining Boots Comfort Shoes Ankle Fashion 5 Boots EU38 Fluff Round Bootie z8BqBf1, 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 frustumVelocity Velocity Women's Women's V V Velocity Women's V .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Velocity V Women's Velocity V Velocity Women's V Women's , 2) +Velocity Velocity V Women's Women's Velocity Women's V V vp(3, 2); frustum.right.D = -vp(For Leather Fashion Shoes Flat Brown Leopard Slouch High CN39 EU39 Winter US8 Outdoor Boots Women'S RTRY Blue Boots Black Heel UK6 Casual Boots Boots Knee Nappa Z5wXxAtx0, 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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