In the formula for the Householder reflection, a (2/n) is missing:

2
A_n = I_n - - U_n
n

Line 16 of article text, a half (1/2) is missing:

"... the desired half life at the low end of the spectrum at f = 0 (DC), and \lambda_H = \lambda( 1/2 f_s ) ..."

the formula for g_i(f) has a missing exponent:

-m_i / \lambda(f)
g_i(f) = 2

line 7 of article text, must read
"... and recalculates the filter alphas \alpha_i from \beta_i' every time dp changes."

"GetObjectManagar() as a global"
Should read
"GetObjectManagar() is a global"

spurious apostrophe in "Dest'royMe()" (should read: "DestroyMe()")

paragraph that begins "The class name will be..."
The "@T:" shouldn't be there.

first paragraph, line 6
The correct equation in the sixth line is O(n) (instead of )

second to last paragraph
"Determining intersection against an axis-align bounding box is almost [...]"
Should read
"Determining intersection against an axis-aligned bounding box is
almost [...]"
(note conjugation of "aligned")

"*** Insert CD Icon Here ***"" -- This text should be deleted.

"Subtraction (_)"
Should read
"Subtraction (-)"

for_each(vertex in m_poins)
Should read
for_each(vertex in m_points)

"Subtraction _"
Should read
"Subtraction -" (note hyphen instead of underscore)

Two changes. Not errors, but the code is a bit confusing

Because of the shadowing of the 'node' variable. The following will make
it more readable:
Page 111, First line of the sample code:
void Bsp::Recurs_Clip(int node,
Should read
void Bsp::Recurs_Clip(int node_idx,

111, fifth line of the sample code
BspNode node = GetNode(node)
Should read
BspNode node = GetNode(node_idx)

Unfortunately the author of this article did not provide the files as referenced here, so there are no files available for the example of the fixed-function style pipeline using recombinant shaders.

The correct equation in the the sixth line is O(n) (instead of ).

Source Code and demo update for article 4.5

On page 204, figure 2.1.3 (basis of CV) the 6th and 7th term should be e1 ^ e3 and e2 ^ e3 .
The examples on page 208, figure 2.1.11 is incorrect, for the given A and B. ie A^B,AB,A_B should be corrected.

In article 1.6 “Improved Frustum Culling"  the formulation is slightly off in cFrustum::ClassifySphere. The radius of the sphere must be divided by the constant value cos(fov/2). In your figure 1.6.7, if you actually move the sphere shown so that its leftmost point touches the  rLimit line, according to the test the sphere is outside the frustum. But actually, the sphere will overlap the frustum along the upper-left edge of the sphere. To make sure the sphere does not overlap the frustum, you need to move it out further than the radius, you need radius/cos(fov/2). Figure attached.

The code for right/left testing would then be something like:

float r = OP * RightVector;
float rLimit = rFactor * f;
float scaledRadius = Radius / cos(fov/2); // this cosine term should

be computed once and saved, of course

if ( r < -rLimit-scaledRadius || rLimit+scaledRadius < r ) return false;

rLimit is the distance from the center line to the edge of the frustum at the sphere's distance from the eye.
Instead of moving out by the radius, you need to move out by a bit more to ensure that the sphere doesn't hit the frustum further out.

Odds are that most people using this code won't notice the problem,
since bounding spheres are rarely tight against the object. But in
theory this problem means that the sphere could be rejected when it
should not be.

Thanks to Eric Haines for this catch.