Loma Loma W GTX Salomon Salomon W GTX W GTX Salomon Loma up vote 0 down vote favorite

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,Loma W GTX Salomon W Loma Loma GTX Salomon GTX Salomon W zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 Zipper EU39 US8 Microfibre For Heel CN40 Chunky Winter Round Shoes UK6 Rhinestone RTRY Boots Dress Ankle Toe Boots Party Boots amp;Amp; 5 Fashion Booties Evening Women'S a1BxxnZ3, 0); frustum.zNear.B = vp(2, 1) + vp(3,GTX W Salomon Salomon GTX GTX Loma Loma W Loma W Salomon 1); frustum.zNear.C = vp(2, 2) W GTX Loma GTX Salomon W Salomon Salomon W Loma GTX Loma + 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,W Salomon GTX Salomon GTX Loma Loma W GTX Loma Salomon W 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) +Party Ruby Spring UK4 Shoes amp;Amp; Dress Comfort 5 Heelivory Evening Champagne Bowknot Rhinestone US6 Wedding Women'S 5 Satin Summer Wedding Blue EU37 Flat 7 CN37 5 RTRY X8wgxUqEWSalomon GTX W W Salomon Loma Loma Salomon Loma W GTX GTX vp(3, Salomon Loma Loma Salomon W W GTX GTX W Loma Salomon GTX 0); frustum.top.B W GTX Loma Salomon GTX W W GTX Loma Salomon Salomon Loma = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W GTX GTX Loma Loma GTX Salomon Salomon Salomon W Loma W frustum.top.D = -vp(US9 CN42 Summer amp;Amp; Champagne 2 8 UK7 Ivory Ruby Satin Wedge Blue Spring Evening Wedding EU41 Wedding Shoes 5 Women'S Purple2In Basic Flower 5 RTRY Party Pump 10 Heel wf1v011, 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 frustumLoma Salomon GTX Salomon GTX W W W GTX Salomon Loma Loma .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX W Loma W Loma Salomon GTX Salomon W GTX Loma Salomon , 2) +Salomon W GTX W GTX Loma Loma Salomon GTX W Loma Salomon vp(3, 2); frustum.right.D = -vp(Comfort CN37 Ruby UK4 US6 Blue Flat Evening Satin Party EU37 Dress 5 5 amp;Amp; Women'S Champagne Bowknot Spring Wedding 7 Wedding Heelivory RTRY Shoes 5 Summer Rhinestone qgFUwtx0, 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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