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Table of Contents
Surfaces
Definition
The surface is the basic 3D geometric entity. At this level, the geometric concept, Surface, is separated from the topological one, (Side). This allows a definition of a surface much larger than the face (analytically, surfaces are usually infinite – cylinders, planes, NURBS, …), and then to restrain them with a Wire.
Plane
A plane is defined by three points:
plane = surfaceset.add( Plane(number, p1, p2, p3) )
Its normal (and therefore the surface orientation) is calculated using the cross product of the vectors:
$\boldsymbol{p_2}-\boldsymbol{p_1}$ et $\boldsymbol{p_3}-\boldsymbol{p_1}$.
p1, p2, p3 | reference towards the Points |
Coons
A Coons is a linear interpolation between four curves. This curves are gathered in a close wire. The wire orientation defines the surface orientation.
coons = surfaceset.add( Coons(number, wire) )
wire | reference towards the Wire |
Ruled Surface
A ruled surface is defined by linearly interpolating the space between two curves. The orientation of these curves sets the surface orientation.
ruled = surfaceset.add( Ruled(number, curve1, curve2) )
curve1, curve2, … | references towards the Curves |
Ruled surfaces can be used to create planes, if the two curves are lines, or cylinders if the curves are arcs.
Nurbs
nur = surfaceset.add( NurbsSurface(number) ) nur.setDegreeU(degU) nur.setDegreeV(degV) nur.push(i1,j1,p1); nur.pushWeight(i1,j1,w1) nur.push(i2, j2, p2); nur.pushWeight(i2, j2, w2) nur.pushKnotU(knotu1) ... nur.pushKnotU(knotu2) nur.pushKnotV(knotv1) ... nur.pushKnotV(knotv2)
degU, degV | degree along U and V |
i1, j1, i2, j2, … | indices of the pole matrix |
p1, p2, … | reference towards the points (poles) |
w1, w2, … | weights |
knotu1, knotu2, … | knot vector along U |
knotv1, knotv2, … | knot vector along V |
Surface of revolution
revsur = surfaceset.add( RevolutionSurface(number, axe, wire) )
where
axe | Line which defines the revolution axis |
wire | Wire which will rotate along tje revolution axis (it cannot touch the axis on its first point and must be coplanar with it). |
Cylinder
c = Cylinder(number, axe, radius, ptGen) #First way to use Cylinder c = Cylinder(number, axe, radius) #Second way to use Cylinder c.setProjType(projType) surfaceset.add( c )
where
axe | Line which defines the cylinder axis | |
radius | cylinder radius | |
ptGen | optional 'Point of the generating line of the cylinder. This point must be situated: WARNING_MESSAGE (see apps.qs.contactCylProj0Point). This point is compulsory if the cylinder has a given rotation. |
| projType'' | = 0 : the surface is finite and limited by the length of the axis = 1 : the surface is infinite |