Possible Planar Cubic Curves errata, first volume

[erich666]

I may have found some errors in the article "Planar Cubic Curves" in the first Graphics Gems book that are not listed in the errata at http://www.realtimerendering.com/resources/GraphicsGems/Errata.GraphicsGems

Page 576:

• The equation g'(0) = mL(dx/dy) = m0 should be g'(0) = mLdx = m0
• The equation g'(1) = mH(dx/dy) = m1 should be g'(1) = mHdx = m1
• After the dy has been removed from the g'(0) and g'(1) equations, dy is no longer referenced anywhere in the article and its definition dy = yH - yL can be removed

Page 577:

• In the first group of equations, the equation d = m1 should be d = y0 like it was written on page 576
• In the second group of equations, the equation d = y0 should be d = 0 since y0 was defined to be 0 in the preceding paragraph

In addition, on page 578, there is this equation:

f(x) = g(clamp(xL, xH, (x - xL)/(xH - xL)))

Since the (x - xL)/(xH - xL) part is remapping x from [xL, xH] to [0, 1], and g(x) seems to be expecting input values between [0, 1], why is the remapped value clamped between [xL, xH]? Shouldn't the remapped value be clamped between [0, 1] instead? I believe that would match the situation in Figure 4, and the equation would be:

f(x) = g(clamp(0, 1, (x - xL)/(xH - xL)))

Sincerely,

Mika Haarahiltunen

[erich666]

Pinged Andrew.

[erich666]

Andrew replies: Everything he says is right or equivalent-but-clearer, so I say all his points are valid.