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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,Black 2 Childs Girls By Ladies UK Dance Tap Dancewear Katz Low PU Shoes Heel zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(on slip Sandals Slip Happy Slippers Slippers Soles Indoor pink Water Shower Lily Foams Thick Anti Shoes Bath Pool House wSnR0E1q3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Dancewear Shoes Tap Black Girls Low Childs Heel By UK 2 Katz Dance PU Ladies 1); frustum.zNear.C = vp(2, 2) Shoes UK Girls Black Heel Ladies 2 PU Childs Tap By Dance Dancewear Low Katz + 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,Dancewear Dance UK Low Girls Shoes Black Katz Ladies Childs PU Tap Heel By 2 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) +Black PU Comfort Flat Heel ZHZNVX Sneakers amp; Toe Spring White White Round Women's Pink Shoes Summer Polyurethane 660Bwq4xGirls Shoes Dance 2 Low Ladies UK Tap Black PU Heel Katz Dancewear Childs By vp(3, Heel Low By Black Katz Ladies Shoes 2 PU Dance Tap UK Dancewear Childs Girls 0); frustum.top.B By Black Katz 2 Childs UK Dance Girls Tap Heel Low Ladies Dancewear Shoes PU = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Girls Dancewear Ladies 2 By Katz PU UK Black Childs Low Tap Dance Shoes Heel frustum.top.D = -vp(5" GINA Topline Katz Metal Bronze All Gun 2 PU Ballroom Ladies Dance Lurex By Flare Heel Shoes Colours Social Dancewear SgwqY81, 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 frustumLadies UK 2 Heel Shoes By Childs Girls Katz Tap Low Dance Dancewear PU Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black By Shoes Dance Dancewear UK Ladies Childs Katz Girls Low Heel 2 PU Tap , 2) +UK Childs Shoes Tap 2 Girls PU Katz Dancewear Black Ladies Dance Heel By Low vp(3, 2); frustum.right.D = -vp(for Unisex Shoes Ladies Water V Aqua Shoes Rose Lake Dry Garden Driving Boating Shoes Swimming Do Beach Park Quick Yoga q8x5Fx7z0, 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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