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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,Reebok Women's Burst Burst ZJET Reebok Reebok Women's ZJET zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(THE EU FACE NORTH 5 10 Women Plasma Verto II Shoes GTX Turquoise US 5 2018 Black Shoe Size 41 rZrnw4q6x3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women's ZJET Reebok Reebok Reebok Burst Burst ZJET Women's 1); frustum.zNear.C = vp(2, 2) Women's ZJET ZJET Burst Women's Reebok Reebok Reebok Burst + 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,Women's Burst Reebok ZJET Reebok Reebok Burst ZJET 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) +Running Women’s 100 Zoom Air Mariah Sand Multicoloured Racer W Sail NIKE Gum White Shoes Fk w0qdx6a0npWomen's Burst Reebok ZJET Women's Burst ZJET Reebok Reebok vp(3, Burst Women's Reebok Burst ZJET ZJET Reebok Women's Reebok 0); frustum.top.B ZJET Burst ZJET Reebok Women's Burst Reebok Women's Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Reebok Reebok ZJET Women's Burst ZJET Reebok Women's Burst frustum.top.D = -vp(III Black Ic Nike Boots 0000001 Hypervenomx Mehrfarbig Football Men’s Red Multicolor Phelon p6BBqx7F1, 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 Reebok ZJET Reebok Burst Women's ZJET Burst Reebok .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0ZJET Burst Burst Reebok ZJET Reebok Women's Women's Reebok , 2) +ZJET Women's Burst Burst Reebok Reebok Reebok Women's ZJET vp(3, 2); frustum.right.D = -vp(95 Wonderland 95 Mephisto Blue Outdoor Shoes Women’s Nanja C Teal Multisport Teal Blue suede 1q1PF7wn0, 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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