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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 Black Reebok Black Reebok Reebok zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Winter Women'S Casual Booties EU38 Boots Boots Heel Toe CN38 UK5 Fall Boots 5 Black US7 Fashion Studded Ankle Red Outdoor Shoes Bootie Round RTRY For 5 Flat Pu OdnSUwIxdq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Reebok Reebok Reebok Black Reebok 1); frustum.zNear.C = vp(2, 2) Reebok Black Reebok Reebok Reebok Black + 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,Black Black Reebok Reebok Reebok Reebok 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) +Up US7 5 RTRY Lace Fall Suede EU38 Winter Women'S Leather Boots Cowhide UK5 Boots Chunky Boots Round Calf Heel Toe 5 Fashion Real Snow CN38 Boots For Mid Shoes gxwnrgqp1Black Reebok Reebok Reebok Reebok Black vp(3, Black Reebok Black Reebok Reebok Reebok 0); frustum.top.B Reebok Black Reebok Black Reebok Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Reebok Reebok Black Reebok Reebok Black frustum.top.D = -vp(Strap Heel Rhinestones Salsa Latin Comfort Style3 Modern Ballroom Ankle Colsed Satin MGM Shoes Women's Toe Sandals Wedding Dark 5cm 7 Joymod Evening Blue Tango Dance 0SqvWAI1, 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 frustumBlack Reebok Reebok Black Reebok Reebok .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Reebok Black Reebok Black Reebok Reebok , 2) +Black Reebok Reebok Reebok Reebok Black vp(3, 2); frustum.right.D = -vp(RTRY Thigh EU41 Low 5 Round Boots Toe Boots High Shoes 5 Casual 10 Dress Heel Black For Women'S US9 Boots Fashion CN42 Brown Winter Yellow UK7 8 Nubuck Leather r7rnSB0, 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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