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The View Matrix is usually built with the "Look At" data, the Eye, Center and Up vectors. And it looks like this (in column major): | ux vx -nx -eyex | | uy vy -ny -eyey | | uz vz -nz -eyez | | 0 0 0 1 | Where u, v and n are the normalized vectors for the camera referential. u is the up vector, n is the direction the camera is looking at and v is ...

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When you rotate your camera you should apply the same rotation matrix to your up vector. That should result in an up vector in the same direction as your view matrix's up direction.

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I believe the simpler way would be to find the collision between the ray caster from the center of the bubble to two imaginary walls which are 1: left wall moved to the right by the radius of the bubble and 2: right wall moved to the left by the radius of the bubble. The point where this ray (center of the bubble) hits any of the two imaginary walls will ...

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Solution for 2D vectors: Vector2 AB = B - A; // Vector from A to B Vector2 A0 = r * AB.normalized; // Vector from A to 0° Vector2 A90 = new Vector2(A0.y, -A0.x); // Vector from A to 90° Vector2 P = A + Sin(alpha) * A90 + Cos(alpha) * A0; // Coordinate of arbitrary point on a circle For arbitrary 3D vectors A and B in 3D space you need coordinates of ...

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If you don't need a strictly physics based solution, bias and gain can be great for giving a nice organic (accel / decel) feel to a simple linear interpolation. http://blog.demofox.org/2012/09/24/bias-and-gain-are-your-friend/ http://demofox.org/biasgain.html

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You could try setting a threshold from the target, and multiplying the object's speed by distance / threshold: acceleration = distance / threshold if (acceleration <= 1) { speed *= acceleration; } Here's an interactive example I threw together quickly: https://dl.dropboxusercontent.com/u/38185080/Flash/Examples/Deceleration.swf Checking gradual ...

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Adapted from this page, which was linked in Eric Lengyel's paper. Given a view matrix, projection matrix, and a point and a normal for the desired plane, it produces the right projection matrix. rplane plane; D3DXPlaneFromPointNormal(&plane, &p, &normal); D3DXMATRIX matClipProj, WorldToProjection; WorldToProjection = matView * matProjection; ...

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I think that the author is describing how to calculate a bounding sphere in a (rather poor, IMHO) roundabout way. I skimmed over the text you linked to and it doesn't make any sense to me, either. The basic concept of a bounding sphere is that the distance between the center of the object and any point on the sphere is always the same. So all you need to ...

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