1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
-- File: Convert_CompPolynomialToPoles.cdl
-- Created: Tue May 30 13:38:39 1995
-- Author: Xavier BENVENISTE
-- <xab@nonox>
---Copyright: Matra Datavision 1995
class CompPolynomialToPoles from Convert
---Purpose: To convert an function (curve) polynomial by span in a BSpline.
--
-- This class uses the following arguments :
-- NumCurves : the number of Polynomial Curves
-- Continuity: the requested continuity for the n-dimensional Spline
-- Dimension : the dimension of the Spline
-- MaxDegree : maximum allowed degree for each composite
-- polynomial segment.
-- NumCoeffPerCurve : the number of coefficient per segments = degree - 1
-- Coefficients : the coefficients organized in the following way
-- [1..<myNumPolynomials>][1..myMaxDegree +1][1..myDimension]
-- that is : index [n,d,i] is at slot
-- (n-1) * (myMaxDegree + 1) * myDimension + (d-1) * myDimension + i
-- PolynomialIntervals : nth polynomial represents a polynomial between
-- myPolynomialIntervals->Value(n,0) and
-- myPolynomialIntervals->Value(n,1)
-- TrueIntervals : the nth polynomial has to be mapped linearly to be
-- defined on the following interval :
-- myTrueIntervals->Value(n) and myTrueIntervals->Value(n+1)
-- so that it represent adequatly the function with the
-- required continuity
uses Array1OfReal from TColStd,
HArray1OfReal from TColStd,
HArray2OfReal from TColStd,
HArray1OfInteger from TColStd,
Array1OfReal from TColStd,
Array2OfReal from TColStd,
Array1OfInteger from TColStd,
Shape from GeomAbs
raises
OutOfRange from Standard,
ConstructionError from Standard
is
Create(NumCurves : Integer ;
Continuity : Integer ;
Dimension : Integer ;
MaxDegree : Integer ;
NumCoeffPerCurve : HArray1OfInteger from TColStd ;
Coefficients : HArray1OfReal from TColStd ;
PolynomialIntervals : HArray2OfReal from TColStd ;
TrueIntervals : HArray1OfReal from TColStd)
raises ConstructionError ;
---Purpose: Warning!
-- Continuity can be at MOST the maximum degree of
-- the polynomial functions
-- TrueIntervals :
-- this is the true parameterisation for the composite curve
-- that is : the curve has myContinuity if the nth curve
-- is parameterized between myTrueIntervals(n) and myTrueIntervals(n+1)
--
-- Coefficients have to be the implicit "c form":
-- Coefficients[Numcurves][MaxDegree+1][Dimension]
--
-- Warning!
-- The NumberOfCoefficient of an polynome is his degree + 1
-- Example: To convert the linear function f(x) = 2*x + 1 on the
-- domaine [2,5] to BSpline with the bound [-1,1]. Arguments are :
-- NumCurves = 1;
-- Continuity = 1;
-- Dimension = 1;
-- MaxDegree = 1;
-- NumCoeffPerCurve [1] = {2};
-- Coefficients[2] = {1, 2};
-- PolynomialIntervals[1,2] = {{2,5}}
-- TrueIntervals[2] = {-1, 1}
Create(NumCurves : Integer ;
Dimension : Integer ;
MaxDegree : Integer ;
Continuity : Array1OfInteger from TColStd ;
NumCoeffPerCurve : Array1OfInteger from TColStd ;
Coefficients : Array1OfReal from TColStd ;
PolynomialIntervals : Array2OfReal from TColStd ;
TrueIntervals : Array1OfReal from TColStd)
---Purpose: To Convert sevral span with different order of Continuity.
-- Warning: The Length of Continuity have to be NumCurves-1
raises ConstructionError;
Create(Dimension : Integer ;
MaxDegree : Integer ;
Degree : Integer ;
Coefficients : Array1OfReal from TColStd ;
PolynomialIntervals: Array1OfReal from TColStd ;
TrueIntervals : Array1OfReal from TColStd)
---Purpose: To Convert only one span.
raises ConstructionError;
Perform(me : in out;
NumCurves : Integer;
MaxDegree : Integer;
Dimension : Integer ;
NumCoeffPerCurve : Array1OfInteger from TColStd ;
Coefficients : Array1OfReal from TColStd;
PolynomialIntervals : Array2OfReal from TColStd ;
TrueIntervals : Array1OfReal from TColStd) is private;
NbPoles(me) returns Integer ;
--
---Purpose: number of poles of the n-dimensional BSpline
--
Poles(me; Poles : in out HArray2OfReal from TColStd) ;
---Purpose: returns the poles of the n-dimensional BSpline
-- in the following format :
-- [1..NumPoles][1..Dimension]
--
Degree(me)
returns Integer ;
NbKnots(me)
returns Integer ;
---Purpose: Degree of the n-dimensional Bspline
Knots(me; K : in out HArray1OfReal from TColStd) ;
---Purpose: Knots of the n-dimensional Bspline
Multiplicities(me; M : in out HArray1OfInteger from TColStd) ;
---Purpose: Multiplicities of the knots in the BSpline
IsDone(me) returns Boolean ;
fields
myFlatKnots : HArray1OfReal from TColStd ;
myKnots : HArray1OfReal from TColStd ;
myMults : HArray1OfInteger from TColStd ;
myPoles : HArray2OfReal from TColStd ;
-- the poles of the n-dimensional Bspline organized in the following
-- fashion
-- [1..NumPoles][1..myDimension]
myDegree : Integer ;
myDone : Boolean ;
end CompPolynomialToPoles ;
|
