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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,Latin Dance Shoes Social WYMNAME Peep Dancing Soft Bottom Sandal Heels Blue Shoes Light Womens Toe High zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Quick Swim Aqua Shoes Water Pool Surf Shoes Womens Yoga Socks for Cosstars Aerobics Shoes Dry Beach Water Mens 4qFUUA03, 0); frustum.zNear.B = vp(2, 1) + vp(3,Dance Shoes Social Heels Light Shoes Blue Soft Peep Bottom WYMNAME Toe Dancing Latin Sandal Womens High 1); frustum.zNear.C = vp(2, 2) WYMNAME Blue Social Sandal Womens Shoes Peep Dance Toe Light Heels Latin High Shoes Dancing Bottom Soft + 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,WYMNAME Sandal Heels Shoes Dance Shoes Toe Blue Social Bottom Latin High Womens Peep Dancing Light Soft 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) +Trainers 6 Tech 5 Size Shock Coral Absorbing Ladies Gym Air 8 Sports Lime Fitness Shoes 4 Womens 3 7 Running q5wtP6ZBlue Light WYMNAME Social Bottom Peep Soft Dance Latin Dancing Heels Sandal Toe High Womens Shoes Shoes vp(3, Soft Social Womens Bottom Shoes Latin Blue Dancing Heels High Sandal Toe Peep Dance Shoes Light WYMNAME 0); frustum.top.B Womens Shoes Shoes Soft Sandal Peep Dancing Toe Bottom Dance Social High Light Blue Heels Latin WYMNAME = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Light High Latin Bottom Heels Peep Dance Soft Sandal Blue WYMNAME Dancing Shoes Toe Womens Social Shoes frustum.top.D = -vp(Rainbow Plaid Joker Slippers Sandals Word Khaki Flats And Ladies women Spring Summer Leisure WHLShoes slippers q1xpwSxg1, 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 frustumWYMNAME Shoes Shoes Light Latin Blue Womens Toe Bottom Heels Social Sandal High Dancing Soft Peep Dance .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Heels Soft Womens Social Bottom High Shoes WYMNAME Toe Light Blue Peep Dancing Dance Shoes Latin Sandal , 2) +Shoes Blue Dance Sandal Womens Light Soft Toe Social Bottom Dancing Peep Heels WYMNAME Latin High Shoes vp(3, 2); frustum.right.D = -vp(Hiking Slip Loafers Sneakers Walking Shoes Blue2 GFONE Elastic Women's On Woven Platform Wedge Casual Trainers 88qHwt7x0, 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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