# Metafor

ULiege - Aerospace & Mechanical Engineering

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doc:user:geometry:user:surfaces

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# Surfaces

## Definition

In Metafor, a Surface is used to build a (Side) limited by a Wire.

The surface orientation, defined by its normal, is important in 3D contact.

## Plane

A plane is defined by three points:

plane = surfaceset.add( Plane(number, p1, p2, p3) )

with

 number user number (unique among surfaces and $\ge 1$) p1, p2, p3 the 3 Points lying on the plane

Its normal (and therefore the surface orientation) is computed using the cross product of vectors $\boldsymbol{p_2}-\boldsymbol{p_1}$ et $\boldsymbol{p_3}-\boldsymbol{p_1}$.

## Coons

A Coons' surface is a linear interpolation between four Curves. These Curves are gathered in a closed Wire. The Wire orientation defines the surface orientation.

coons = surfaceset.add( Coons(number, wire) )

with

 number user number (unique among surfaces and $\ge 1$) wire the Wire which is interpolated

## Ruled Surface

A ruled surface is defined by linearly interpolating two curves. The orientation of these curves sets the surface orientation.

ruled = surfaceset.add( Ruled(number, curve1, curve2) )

with

 number user number (unique among surfaces and $\ge 1$) curve1, curve2, … the 2 facing Curves

Ruled surfaces can be used to create planes, if the two Curves are coplanar 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) 

with

 number user number (unique among surfaces and $\ge 1$) degU, degV degree along U and V i1, j1, i2, j2, … indices of the pole matrix p1, p2, … points (called “poles”) w1, w2, … weights knotu1, knotu2, … knot vector along U knotv1, knotv2, … knot vector along V

## Closed Surface of revolution

revsur = surfaceset.add( RevolutionSurface(number, axe, wire) )

with

 number user number (unique among surfaces and $\ge 1$) axe Line which defines the revolution axis wire Wire which will rotate along the revolution axis (it cannot intersect the axis on its first point and must be coplanar with it).

## Open Surface of revolution

openrevsur = surfaceset.add( OpenRevolutionSurface(number, axe, wire, angle) )

with

 number User number (unique among surfaces and $\ge 1$) axe Line which defines the revolution axis wire Wire which will rotate along the revolution axis (it cannot intersect the axis on its first point and must be coplanar with it). angle Opening angle $]0, 2 \pi[$

## Sphere

c = Sphere(number, centerPoint, radius, reversed)

with

 number user number (unique among surfaces and $\ge 1$) centerPoint sphere center (Point previously defined in the Pointset !) radius sphere radius reversed unit normal convention - By default (reversed = false), the local covariant tangents are oriented in such a manner that the unit normal points inwards !

## Cylinder

c = Cylinder(number, axis, radius, ptGen) # First way to use Cylinder

c = Cylinder(number, axis, radius)        # Second way to use Cylinder
c.setProjType(projType)

with

 number user number (unique among surfaces and $\ge 1$) axis Line which defines the cylinder axis radius cylinder radius ptGen optional Point of the generating line of the cylinder. This point must be situated: - in a plane perpendicular to the axis including the first point of the axis, - to a distance equal to the cylinder radius of the first point of the axis. Since this point is quite difficult to define when the cylinder is not parallel to an axis, a random point can be supplied and Metafor will put it in its right place with a 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