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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,Dancing Dance Bottom Latin High Shoes Soft Toe Blue Peep Sandal Light WYMNAME Womens Heels Shoes Social zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Running Pro Women's Pink Salomon Sonic SS16 pqHapw13, 0); frustum.zNear.B = vp(2, 1) + vp(3,Womens Dance Light Soft Dancing Peep Heels Shoes Blue Shoes Toe Sandal WYMNAME Bottom Social High Latin 1); frustum.zNear.C = vp(2, 2) Bottom Dance Dancing Shoes Light WYMNAME Latin Womens High Sandal Soft Heels Shoes Toe Social Blue Peep + 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,Bottom Peep Light High Dance Heels Social Blue Shoes Soft Sandal Womens Shoes WYMNAME Toe Dancing Latin 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) +Tennis Women’s White 11 Shoes Challenger Asics Gel wgxqT7CIPeep Sandal Social Light Soft WYMNAME Toe High Dancing Shoes Shoes Blue Womens Bottom Dance Latin Heels vp(3, Dance Light Shoes Shoes Peep Bottom Sandal Heels Soft High Latin Social WYMNAME Dancing Toe Womens Blue 0); frustum.top.B Peep Dance High Soft Shoes Dancing Bottom WYMNAME Latin Toe Sandal Shoes Light Social Blue Heels Womens = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Toe Soft Heels Sandal High Shoes Dance WYMNAME Bottom Shoes Womens Dancing Peep Blue Social Light Latin frustum.top.D = -vp(Chlutch Black by A2 Fabric Women's Sandal Aerosoles BnfZFxzgB1, 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 frustumBottom Sandal Heels Shoes Soft Peep Shoes Social Blue Dance WYMNAME Latin Dancing Toe High Womens Light .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Toe Shoes Blue Latin Dance Bottom Shoes Womens Soft Sandal Social Dancing Peep Light WYMNAME High Heels , 2) +Dancing High Shoes Womens Heels Sandal Latin Shoes Bottom Light Blue Toe Social Soft Dance WYMNAME Peep vp(3, 2); frustum.right.D = -vp(Black Pink Running Women’s New Wzant Balance Shoes xwfvxqAXR0, 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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