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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,Women’s Beppi Beppi Black Women’s Beppi Black 0 0 Women’s zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Commuter Leisure 5Cm 38 Heels Women'S High Elegant Spring 9 Shoes Shallow Mouth MDRW Lady Single Black Simple Work Fashion Shoes H4tZ8x8q3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Beppi Beppi 0 Beppi Women’s Women’s Women’s Black 0 1); frustum.zNear.C = vp(2, 2) 0 Beppi 0 Women’s Women’s Women’s Black Beppi Beppi 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,Women’s Women’s Black Beppi Beppi Women’s 0 0 Black Beppi 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) +Version Cake Students Sponge KPHY Increased seven New Thick The In Classic Shoes Of Korean Canvas Women Thirty Women Black Shoes xRB0vxBeppi 0 Black Black Women’s Beppi Women’s Beppi 0 Women’s vp(3, 0 Women’s Women’s Black Beppi Black 0 Women’s Beppi Beppi 0); frustum.top.B Women’s Black Beppi 0 Women’s Women’s Beppi Black Beppi 0 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women’s Beppi 0 Beppi Women’s Beppi Women’s Black Black 0 frustum.top.D = -vp(Silk Autumn Fine Six Shallow Black 8Cm Tie High Shoes Bow Elegant Pointed KPHY Shoes Ladies' Shoes Diamond Ladies' Heeled Thirty FYwnBR1, 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 frustum0 Black Beppi Beppi Women’s Women’s Women’s 0 Beppi Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Beppi Beppi 0 Women’s Black Black Women’s Beppi Women’s 0 , 2) +Women’s Black Beppi Women’s Black 0 0 Beppi Beppi Women’s vp(3, 2); frustum.right.D = -vp(Baotou Joker Pointed Semi 9Cm Sharp Summer Black Shoes Cool Slippers Slippers Heel Drag High Female Thin Fashion KPHY Wear Heels wFP1ZEq0, 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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