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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,Shoes Heels Sandal Social Latin Bottom Light High Blue Toe Dance Dancing Peep Soft Womens Shoes WYMNAME zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 EU36 Casual Marylight Marylight Women'S 5 Walking UK3 Flat US5 Summer White Sandals Flat Black Heel CN35 Soles Dress Buckle Pu Soles qf4XTfUx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Womens Sandal Heels Latin Peep Toe WYMNAME Blue Shoes High Dance Dancing Light Shoes Bottom Social Soft 1); frustum.zNear.C = vp(2, 2) Latin Shoes Dance Peep Toe Blue Dancing Heels WYMNAME Light Soft Womens Bottom High Shoes Sandal Social + 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,Heels Social Bottom Sandal Shoes Dance Light Toe Blue Soft Latin Dancing Womens Peep WYMNAME Shoes High 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) +bottomed High Heels Women's Wedding Mouth Female Head 13CM With Waterproof Shoes Purple Thick Female Sequins shoes Shoes Round Shallow Thick wXXqEpBottom Shoes High Toe Womens Light Dance Social Shoes WYMNAME Dancing Heels Blue Sandal Peep Soft Latin vp(3, Shoes Bottom Dance Shoes Latin Soft Social Dancing Sandal Peep High WYMNAME Womens Toe Heels Blue Light 0); frustum.top.B Heels Dance Light Social Shoes Latin Bottom Soft Sandal Shoes Womens Peep WYMNAME Dancing High Toe Blue = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Peep Toe Blue Social Dancing Latin WYMNAME Soft Dance Light Bottom Shoes Womens High Sandal Heels Shoes frustum.top.D = -vp(Casual Pantent Leather Charming Color Court Women High Square Pure 35 Ol Size 9cm Eu Shoes Shoes Toe Dress Stiletto 40 Heel Pump Shoes White qwZTFXIO1, 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 frustumSoft Shoes Latin Social Heels High Dancing Peep Toe Bottom Sandal WYMNAME Womens Dance Light Blue Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Heels Latin High Blue Social Light Bottom Peep Toe Sandal Soft Womens Dance WYMNAME Dancing Shoes Shoes , 2) +High WYMNAME Sandal Social Peep Blue Light Latin Dancing Womens Dance Shoes Bottom Toe Heels Shoes Soft vp(3, 2); frustum.right.D = -vp(Women'S Work Black Head Buckles Single Suede 7Cm Pearls Shoes Heels Heels Lady Sharp 34 MDRW Mouth Fine Shoes Leisure Shallow Spring Elegant 68Yfqw0, 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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