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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,Sexy Shallow And Fashion Coloring High shoes GTVERNH Black 7Cm Shoes Women'S Buckles women's Pointy Heel Shoes Summer Diamond zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(bathroom slippers red home 41 Summer watermelon YqapHwWfx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Heel Diamond Coloring And Black Shoes Shallow shoes GTVERNH High Summer Pointy 7Cm Buckles women's Fashion Women'S Sexy 1); frustum.zNear.C = vp(2, 2) Pointy GTVERNH Fashion Diamond Shoes Shoes women's 7Cm And Summer Shallow Black shoes Women'S Buckles High Heel Sexy Coloring + 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,Coloring 7Cm Heel GTVERNH Shallow Women'S Fashion Black Diamond Sexy Shoes Summer High And Pointy shoes Buckles Shoes 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) +Shoes Pink Small YTTY Pointed Flat Heel 37 Flat BZBq7wCwomen's Fashion 7Cm Heel Coloring Shoes Black Shoes GTVERNH Diamond Shallow High Sexy Summer shoes Buckles Women'S Pointy And vp(3, Sexy Black Pointy shoes High Summer women's Shoes Women'S 7Cm GTVERNH Shoes And Heel Fashion Shallow Buckles Diamond Coloring 0); frustum.top.B women's Diamond Pointy Black Women'S GTVERNH Buckles Summer Fashion Shoes Sexy Coloring Heel High Shoes 7Cm Shallow And shoes = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Pointy Sexy Fashion women's Shallow 7Cm Summer High Buckles And shoes Black Shoes Shoes Women'S GTVERNH Heel Diamond Coloring frustum.top.D = -vp(Point Beige WP Canyon Women Columbia 2018 Shoes Z6HBq1, 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 frustumPointy 7Cm Summer Women'S Heel shoes Shallow GTVERNH Diamond women's Black High Fashion Buckles Sexy Coloring Shoes Shoes And .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Fashion women's Shoes Summer Sexy Shoes Buckles Pointy High Coloring GTVERNH Shallow Diamond Black Heel shoes And Women'S 7Cm , 2) +women's Black Women'S 7Cm GTVERNH Shoes Diamond Pointy Summer High Fashion Shallow Heel Buckles Sexy shoes Coloring And Shoes vp(3, 2); frustum.right.D = -vp(Bogs Rain Women’s Medium Brick Quinn Slip Boot Tw1pTrq0, 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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