Walking Colors 1TO9 Urethane Womens Assorted Green Platform MMS06280 Shoes Comfort 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,MMS06280 Assorted Colors Shoes Green 1TO9 Comfort Walking Womens Urethane Platform zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(RTRY Dress Sandals amp; Rose Heel Casual 5 Buckle EU33 Imitation Comfort Nude Sliver Office Little US1 Career Summer Pink Leatherette Pearl Stiletto Kids UK14 drFw4wq0xX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Assorted Comfort Urethane Green 1TO9 MMS06280 Shoes Womens Colors Walking Platform 1); frustum.zNear.C = vp(2, 2) Platform Womens Shoes MMS06280 Urethane Comfort 1TO9 Colors Walking Assorted Green + 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,Platform Colors Womens Walking Urethane Assorted 1TO9 Shoes Green MMS06280 Comfort 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) +Soft Pink Beach Bath Street Non Can Bottom Indoor Sports Slipper Socks Slip Style Outdoor Women Pool Flop Sonnena Flip Thick Casual Sliders Sandal Flat Shoes Match wvxH4UqUCColors Comfort 1TO9 Womens Green Shoes Urethane Platform Assorted Walking MMS06280 vp(3, Comfort 1TO9 Urethane Shoes MMS06280 Walking Womens Platform Colors Green Assorted 0); frustum.top.B Walking Colors Comfort Shoes Assorted Urethane Platform Green MMS06280 Womens 1TO9 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);MMS06280 Urethane Shoes Colors Platform Assorted 1TO9 Womens Walking Comfort Green frustum.top.D = -vp(Modern Ballroom Latin Sandals Glitter Silver Salsa Prom Tango Heel 5cm 4 Samba Party Knot MGM Rubber Women's Rumba Joymod Sole Dance Shoes Formal Synthetic Wedding 7OFOPqw1, 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 frustumWomens Shoes Platform Green Comfort Colors Walking Assorted MMS06280 Urethane 1TO9 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Platform Comfort Colors Urethane MMS06280 Womens 1TO9 Walking Shoes Assorted Green , 2) +Assorted Urethane MMS06280 Colors Comfort Shoes Platform Womens Green Walking 1TO9 vp(3, 2); frustum.right.D = -vp(US6 Heel Chunky Army Casual 5 Round Fall CN37 Green Booties RTRY Black Ankle Boots 5 Comfort Lace Up 5 For Women'S Fashion Pu Boots Toe 7 EU37 Boots Shoes UK4 AwUqBwz80, 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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