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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,Lace Ankle Lisboa nbsp; Up Hobo Boots zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Blue Running Shoes Women’s Black 4 Brooks Aduro Pink Blue Spectrum Glo Xqwf1HTO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,nbsp; Hobo Up Boots Ankle Lace Lisboa 1); frustum.zNear.C = vp(2, 2) Lisboa Hobo Boots nbsp; Up Ankle Lace + 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,Ankle Boots Lisboa nbsp; Up Lace Hobo 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) +Icepeak Au Multisport 065 Wolter Outdoor Lait Cafe Brown Shoes Women’s gZgxrRLace Lisboa Hobo Up Boots Ankle nbsp; vp(3, Lisboa Lace Boots Up Ankle nbsp; Hobo 0); frustum.top.B Ankle nbsp; Boots Hobo Lisboa Lace Up = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);nbsp; Hobo Lisboa Ankle Up Boots Lace frustum.top.D = -vp(Women’s Guide Iso Black Shoes Red Competition Saucony Vizired 2 Running pFxwnfqF41, 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 frustumHobo nbsp; Up Lisboa Ankle Boots Lace .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Ankle Up Lisboa nbsp; Boots Lace Hobo , 2) +Lisboa Ankle nbsp; Boots Up Lace Hobo vp(3, 2); frustum.right.D = -vp(Blue Soft Shoes Women's 16 Blue Cumulus Gel Asics Running Deep Nectarine 7wZqBv6x0, 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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