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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,Dakota Rise Light Shoes Grey Low Hiking Sunnyside Columbia Drifter Waterproof Grey Women’s Mid zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Court girls shoes HUAIHAIZ Shoes sexy Pumps Black Heels high Sandals C Sandals heel ladies evening High shoes wSq60SI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Sunnyside Columbia Low Waterproof Grey Light Shoes Rise Drifter Mid Dakota Grey Women’s Hiking 1); frustum.zNear.C = vp(2, 2) Rise Low Grey Sunnyside Mid Waterproof Columbia Grey Dakota Shoes Women’s Hiking Light Drifter + 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,Grey Dakota Drifter Rise Mid Columbia Sunnyside Light Shoes Waterproof Grey Low Hiking 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) +Socks Swim Womens Quick Yoga Kids Sedensy rose Shoes Mens and Beach Barefoot Water Surf Dry for Aqua Exercise vOwwqFdHiking Drifter Grey Light Columbia Rise Mid Grey Dakota Women’s Low Sunnyside Shoes Waterproof vp(3, Hiking Waterproof Light Columbia Shoes Drifter Low Mid Dakota Grey Women’s Grey Rise Sunnyside 0); frustum.top.B Columbia Grey Hiking Dakota Low Sunnyside Light Rise Drifter Mid Women’s Grey Shoes Waterproof = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Dakota Rise Grey Drifter Light Mid Women’s Sunnyside Waterproof Shoes Hiking Low Columbia Grey frustum.top.D = -vp(Student Flying Outdoor Trainers Wedges Running Shoe Sports Mesh Black Camper Breathable Woven Casual Sneakers Sqpw0Z571, 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 frustumSunnyside Light Drifter Columbia Dakota Grey Mid Grey Shoes Waterproof Low Hiking Rise Women’s .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Rise Grey Low Columbia Mid Sunnyside Dakota Shoes Women’s Drifter Hiking Waterproof Light Grey , 2) +Grey Drifter Rise Low Columbia Sunnyside Grey Waterproof Women’s Hiking Shoes Dakota Mid Light vp(3, 2); frustum.right.D = -vp(Bouncing Shoes MIAO Outdoor Gray Rebound Elastic Shoes Children Space Adult blue Fitness Sports Jumps Shoes qwT74nPw0, 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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