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1 | -- Created on: 1993-03-10 |
2 | -- Created by: JCV |
3 | -- Copyright (c) 1993-1999 Matra Datavision |
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4 | -- Copyright (c) 1999-2014 OPEN CASCADE SAS |
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5 | -- |
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6 | -- This file is part of Open CASCADE Technology software library. |
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7 | -- |
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8 | -- This library is free software; you can redistribute it and/or modify it under |
9 | -- the terms of the GNU Lesser General Public License version 2.1 as published |
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10 | -- by the Free Software Foundation, with special exception defined in the file |
11 | -- OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT |
12 | -- distribution for complete text of the license and disclaimer of any warranty. |
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13 | -- |
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14 | -- Alternatively, this file may be used under the terms of Open CASCADE |
15 | -- commercial license or contractual agreement. |
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16 | |
17 | class Parabola from Geom inherits Conic from Geom |
18 | |
19 | ---Purpose : Describes a parabola in 3D space. |
20 | -- A parabola is defined by its focal length (i.e. the |
21 | -- distance between its focus and its apex) and is |
22 | -- positioned in space with a coordinate system |
23 | -- (gp_Ax2 object) where: |
24 | -- - the origin is the apex of the parabola, |
25 | -- - the "X Axis" defines the axis of symmetry; the |
26 | -- parabola is on the positive side of this axis, |
27 | -- - the origin, "X Direction" and "Y Direction" define the |
28 | -- plane of the parabola. |
29 | -- This coordinate system is the local coordinate |
30 | -- system of the parabola. |
31 | -- The "main Direction" of this coordinate system is a |
32 | -- vector normal to the plane of the parabola. The axis, |
33 | -- of which the origin and unit vector are respectively the |
34 | -- origin and "main Direction" of the local coordinate |
35 | -- system, is termed the "Axis" or "main Axis" of the parabola. |
36 | -- The "main Direction" of the local coordinate system |
37 | -- gives an explicit orientation to the parabola, |
38 | -- determining the direction in which the parameter |
39 | -- increases along the parabola. |
40 | -- The Geom_Parabola parabola is parameterized as follows: |
41 | -- P(U) = O + U*U/(4.*F)*XDir + U*YDir |
42 | -- where: |
43 | -- - P is the point of parameter U, |
44 | -- - O, XDir and YDir are respectively the origin, "X |
45 | -- Direction" and "Y Direction" of its local coordinate system, |
46 | -- - F is the focal length of the parabola. |
47 | -- The parameter of the parabola is therefore its Y |
48 | -- coordinate in the local coordinate system, with the "X |
49 | -- Axis" of the local coordinate system defining the origin |
50 | -- of the parameter. |
51 | -- The parameter range is ] -infinite, +infinite [. |
52 | |
53 | uses Ax1 from gp, |
54 | Ax2 from gp, |
55 | Parab from gp, |
56 | Pnt from gp, |
57 | Trsf from gp, |
58 | Vec from gp, |
59 | Geometry from Geom |
60 | |
61 | raises ConstructionError from Standard, |
62 | RangeError from Standard |
63 | |
64 | |
65 | is |
66 | |
67 | |
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68 | Create (Prb : Parab) returns Parabola; |
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69 | ---Purpose : Creates a parabola from a non transient one. |
70 | |
71 | |
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72 | Create (A2 : Ax2; Focal : Real) returns Parabola |
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73 | ---Purpose : |
74 | -- Creates a parabola with its local coordinate system "A2" |
75 | -- and it's focal length "Focal". |
76 | -- The XDirection of A2 defines the axis of symmetry of the |
77 | -- parabola. The YDirection of A2 is parallel to the directrix |
78 | -- of the parabola. The Location point of A2 is the vertex of |
79 | -- the parabola |
80 | raises ConstructionError; |
81 | ---Purpose : Raised if Focal < 0.0 |
82 | |
83 | |
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84 | Create (D : Ax1; F : Pnt) returns Parabola; |
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85 | ---Purpose : |
86 | -- D is the directrix of the parabola and F the focus point. |
87 | -- The symmetry axis (XAxis) of the parabola is normal to the |
88 | -- directrix and pass through the focus point F, but its |
89 | -- location point is the vertex of the parabola. |
90 | -- The YAxis of the parabola is parallel to D and its location |
91 | -- point is the vertex of the parabola. The normal to the plane |
92 | -- of the parabola is the cross product between the XAxis and the |
93 | -- YAxis. |
94 | |
95 | |
96 | |
97 | SetFocal (me : mutable; Focal : Real) |
98 | ---Purpose : Assigns the value Focal to the focal distance of this parabola. |
99 | -- Exceptions Standard_ConstructionError if Focal is negative. |
100 | raises ConstructionError |
101 | is static; |
102 | |
103 | |
104 | SetParab (me : mutable; Prb : Parab) |
105 | ---Purpose: Converts the gp_Parab parabola Prb into this parabola. |
106 | |
107 | is static; |
108 | |
109 | |
110 | Parab (me) returns Parab |
111 | ---Purpose : |
112 | -- Returns the non transient parabola from gp with the same |
113 | -- geometric properties as <me>. |
114 | is static; |
115 | |
116 | |
117 | ReversedParameter(me; U : Real) returns Real is redefined static; |
118 | ---Purpose: Computes the parameter on the reversed parabola, |
119 | -- for the point of parameter U on this parabola. |
120 | -- For a parabola, the returned value is: -U. |
121 | |
122 | |
123 | FirstParameter (me) returns Real is redefined static; |
124 | ---Purpose : Returns the value of the first or last parameter of this |
125 | -- parabola. This is, respectively: |
126 | -- - Standard_Real::RealFirst(), or |
127 | -- - Standard_Real::RealLast(). |
128 | |
129 | LastParameter (me) returns Real is redefined static; |
130 | ---Purpose : Returns the value of the first or last parameter of this |
131 | -- parabola. This is, respectively: |
132 | -- - Standard_Real::RealFirst(), or |
133 | -- - Standard_Real::RealLast(). |
134 | |
135 | IsClosed (me) returns Boolean is redefined static; |
136 | ---Purpose : Returns False |
137 | |
138 | |
139 | IsPeriodic (me) returns Boolean is redefined static; |
140 | ---Purpose : Returns False |
141 | |
142 | |
143 | Directrix (me) returns Ax1; |
144 | ---Purpose : Computes the directrix of this parabola. |
145 | -- This is a line normal to the axis of symmetry, in the |
146 | -- plane of this parabola, located on the negative side |
147 | -- of its axis of symmetry, at a distance from the apex |
148 | -- equal to the focal length. |
149 | -- The directrix is returned as an axis (gp_Ax1 object), |
150 | -- where the origin is located on the "X Axis" of this parabola. |
151 | |
152 | |
153 | |
154 | Eccentricity (me) returns Real is redefined static; |
155 | ---Purpose : Returns 1. (which is the eccentricity of any parabola). |
156 | |
157 | |
158 | Focus (me) returns Pnt; |
159 | ---Purpose: Computes the focus of this parabola. The focus is on the |
160 | -- positive side of the "X Axis" of the local coordinate |
161 | -- system of the parabola. |
162 | |
163 | Focal (me) returns Real; |
164 | ---Purpose : Computes the focal distance of this parabola |
165 | -- The focal distance is the distance between the apex |
166 | -- and the focus of the parabola. |
167 | |
168 | |
169 | Parameter (me) returns Real; |
170 | ---Purpose : Computes the parameter of this parabola which is the |
171 | -- distance between its focus and its directrix. This |
172 | -- distance is twice the focal length. |
173 | -- If P is the parameter of the parabola, the equation of |
174 | -- the parabola in its local coordinate system is: Y**2 = 2.*P*X. |
175 | |
176 | |
177 | |
178 | D0(me; U : Real; P : out Pnt) is redefined static; |
179 | ---Purpose: Returns in P the point of parameter U. |
180 | -- If U = 0 the returned point is the origin of the XAxis and |
181 | -- the YAxis of the parabola and it is the vertex of the parabola. |
182 | -- P = S + F * (U * U * XDir + * U * YDir) |
183 | -- where S is the vertex of the parabola, XDir the XDirection and |
184 | -- YDir the YDirection of the parabola's local coordinate system. |
185 | |
186 | |
187 | D1 (me; U : Real; P : out Pnt; V1 : out Vec) is redefined static; |
188 | ---Purpose : |
189 | -- Returns the point P of parameter U and the first derivative V1. |
190 | |
191 | |
192 | D2 (me; U : Real; P : out Pnt; V1, V2 : out Vec) is redefined static; |
193 | ---Purpose : |
194 | -- Returns the point P of parameter U, the first and second |
195 | -- derivatives V1 and V2. |
196 | |
197 | |
198 | D3 (me; U : Real; P : out Pnt; V1, V2, V3 : out Vec) is redefined static; |
199 | ---Purpose : |
200 | -- Returns the point P of parameter U, the first second and third |
201 | -- derivatives V1 V2 and V3. |
202 | |
203 | |
204 | DN (me; U : Real; N : Integer) returns Vec |
205 | ---Purpose : For the point of parameter U of this parabola, |
206 | -- computes the vector corresponding to the Nth derivative. |
207 | -- Exceptions Standard_RangeError if N is less than 1. |
208 | raises RangeError |
209 | is redefined static; |
210 | |
211 | |
212 | Transform (me : mutable; T : Trsf) is redefined static; |
213 | ---Purpose: Applies the transformation T to this parabola. |
214 | |
215 | TransformedParameter(me; U : Real; T : Trsf from gp) returns Real |
216 | ---Purpose: Returns the parameter on the transformed curve for |
217 | -- the transform of the point of parameter U on <me>. |
218 | -- |
219 | -- me->Transformed(T)->Value(me->TransformedParameter(U,T)) |
220 | -- |
221 | -- is the same point as |
222 | -- |
223 | -- me->Value(U).Transformed(T) |
224 | -- |
225 | -- This methods returns <U> * T.ScaleFactor() |
226 | is redefined static; |
227 | |
228 | ParametricTransformation(me; T : Trsf from gp) returns Real |
229 | ---Purpose: Returns a coefficient to compute the parameter on |
230 | -- the transformed curve for the transform of the |
231 | -- point on <me>. |
232 | -- |
233 | -- Transformed(T)->Value(U * ParametricTransformation(T)) |
234 | -- |
235 | -- is the same point as |
236 | -- |
237 | -- Value(U).Transformed(T) |
238 | -- |
239 | -- This methods returns T.ScaleFactor() |
240 | is redefined static; |
241 | |
242 | |
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243 | Copy (me) returns like me |
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244 | is redefined static; |
245 | ---Purpose: Creates a new object which is a copy of this parabola. |
246 | fields |
247 | |
248 | focalLength : Real; |
249 | |
250 | end; |