Submitter: Henderson

Addressed to: JTC1/SC 24/WG 6 Rapporteur Group on ISO/IEC 8632, CGM

WG secretariat: NNI

Date Circulated by WG secretariat: 21 July 1998

Deadline on response from editor: : 3 August 1998

Defect Report concerning IS 8632:1992 Computer Graphics: Metafile for the storage and transfer of picture description information (CGM) Part 1, Functional

specification.

Qualifier (e.g. error, omission, clarification required): Correction

References in document (e.g. page, clause, figure and/or table numbers): clause 4.6.10.1.2, page 46; clause 5.6.24, page 183; and clause 5.6.25, page 183-4.

Nature of defect (complete, concise explanation of the perceived problem):

There are mistakes in the equations for NURBS and NUBS, clause 4.6.10.2, page 46.

In the Parameters section of clauses 5.6.24 and 5.6.25, the order of the spline is apparently designated by "m". But in the Description section, "m" is undefined and the order is designated by "k".

The CGM defects editor has convened an ad hoc committee of NURBS and CGM experts. The ad hoc committee achieved the following consensus on corrections.

The i-th control point will be written P[i], designating P_sub_i

The j-th knot will be written T[j], designating T_sub_j

The i-th B-spline basis function of order k will be written B[i,k], designating B_super_k_sub_i.

1. On page 46, Equation 1, change the lower limit of the sum from "i=0" to "i=1".

2. On page 46, clause 4.6.10.1.2, replace the sentence

"The knot vector consists of a non-decreasing sequence of real numbers (T[1],...,T[n+k]) such that T[i] <= T[i+1] for all i=1,...,n"

with

"The knot vector consists of a non-decreasing sequence of real numbers (T[1],...,T[n+k])."

3. On page 46, clause 4.6.10.1.2, replace the sentence which begins "The curve itself is defined...", with

"The curve itself is defined for the range T[k] <= t <= T[n+1] and can be confined to the range [Tmin, Tmax], where T[k] <= Tmin <= Tmax <= T[n+1]."

4. On page 46, clause 4.6.10.1.2, change the recursive definition of B-spline basis functions as follows

The B-spline basis functions are defined by the recursive relation:

1, if T[i] <= t < T[i+1]

B[i,1](t) =

0, otherwise

and for k > 1

0, if t < T[i] or t > T[i+k]

B[i,k](t) =

(t-T[i])*B[ i,k-1](t) (T[i+k]-t)*B[i+1,k-1](t)

---------------------- + --------------------------- , if T[i] <= t <= T[i+k]

T[i+k-1] - T[i] T[i+k] - T[i+1]

5. On page 47, Equation 2, change the lower limit of both sums, from "i=0" to "i=1".

In the parameters section of clauses 5.6.24 and 5.6.25, change "(m+n)" to "(k+n)".

Amend the standard as proposed above.