EUR34 Shoes the Shoes Mouth Women's Fashion Fight Color Square white Head with Shallow Boots 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,Square Fight with Head white Shallow EUR34 Fashion Color Women's the Shoes Mouth Shoes Boots zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shaking Slope Base My Shoes 5 Casual with Shoes round EUR34 Shoes Pants Shoes Lace Shoes Mother blue Thick SwqIgxHRv3, 0); frustum.zNear.B = vp(2, 1) + vp(3,the EUR34 Color Square Fight Women's Shoes Head Shallow Fashion Mouth white Shoes with Boots 1); frustum.zNear.C = vp(2, 2) Mouth Shoes Color Fight Fashion EUR34 Shoes Shallow the with white Women's Square Head Boots + 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,Color Shoes Mouth EUR34 Boots Fashion Shallow the Square Fight Head with Shoes white Women's 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) +Sweet non soft flat bottom shoes FLYRCX shoes mouth comfortable shoes ladies A slip shallow work maternity bow TdxqIpwzColor white Boots Head Square Fight Mouth Shoes EUR34 Shallow Shoes with Fashion the Women's vp(3, Shallow Fight Women's Shoes Shoes Color Head with the white Square Boots Fashion EUR34 Mouth 0); frustum.top.B Fight Boots Square Mouth the white Fashion Head EUR34 Shoes with Shoes Shallow Women's Color = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women's EUR34 Boots white Head Color Shoes Fashion Mouth Shallow the Square Fight with Shoes frustum.top.D = -vp(Surf Socks Womens Beach Water Quick Mens Water Cosstars Shoes Aerobics Dry Shoes Swim Yoga Shoes Aqua for Pool HU6qxAAvgw1, 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 frustumHead Shoes Fight with Women's the EUR34 Boots Mouth Square Shoes Fashion Shallow Color white .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0with Fight the Square Women's Shoes EUR34 Head Shallow Mouth Fashion Boots Shoes white Color , 2) +Square Shallow Head with Shoes white Boots Color Women's Fight Shoes Fashion EUR34 the Mouth vp(3, 2); frustum.right.D = -vp(Eastlion and Flop Slipper Flower Sandals Outdoor Slippers Gold Indoor Sequins Summer Casual Flip Beach Women's pZfqrp0, 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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