Rhino 3D V1 - Rum


Rhino 3D V1 - Rum

Rhino 3D V1

04/10/2010 AAA

A short introduction to simple 3D geometry

in McNeels Rhinoceros 4.0.


Rhino_2D Modul 1


V-Ray t. Rhino

Modul 2

Modul 2


Modul 3


Photoshop Adv.

Modul 3

Modul 3





3D studio max

Script compiler


Render software.




3D studio max





Excel og lign.

Excel og lign.













Non-Uniform Rational B-Spline

Non-Uniform Rational B-Spline (NURBS)

What kind of a word is “NURBS”?

The word NURBS is an acronym for non-uniform rational B spline. Non uniform rational B splines can represent 3 D geometry.

Why use NURBS to represent 3 D geometry?

NURBS geometry has five important qualities that make it an ideal choice for computer aided modeling.

There are several industry standard ways to exchange NURBS geometry. This means that customers can and should expect to be able to move their valuable

geometric models between various modeling, rendering, animation, and engineering analysis programs. They can store geometric information in a way that will

be usable 20 years from now.

NURBS have a precise and well-known definition. The mathematics and computer science of NURBS geometry is taught in most major universities. This

means that specialty software vendors, engineering teams, industrial design firms, and animation houses that need to create custom software applications, can

find trained programmers who are able to work with NURBS geometry.

NURBS can accurately represent both standard geometric objects like lines, circles, ellipses, spheres, and tori, and free-form geometry like car bodies and human


The amount of information required for a NURBS representation of a piece of geometry is much smaller than the amount of information required by common

faceted approximations.

The NURBS evaluation rule, discussed below, can be implemented on a computer in a way that is both efficient and accurate.

What is NURBS geometry?

There are lots of ways to answer to this question. If you are comfortable reading mathematical formulae, then you can get more detailed information by going

to the Books and papers on NURBS section at the openNURBS web site (http://www.opennurbs.com/books.htm) and clicking on the links

Rhino uses NURBS to represent curves and surfaces. NURBS curves and surfaces behave in similar ways and share a lot of terminology. Since curves are easiest

to describe, we will cover them in detail. Rhino has surface tools that are analogous to the curve tools mentioned below.

A NURBS curve is defined by four things: degree, control points, knots, and an evaluation rule.

The degree is a positive whole number.

This number is usually 1, 2, 3 or 5. Rhino lines and polylines are degree 1, Rhino circles are degree 2, and most Rhino free-form curves are degree 3 or 5.

Rhino will let you work with NURBS that have degrees from 1 to 11. Sometimes the terms linear, quadratic, cubic, and quintic are used. Linear means degree

1, quadratic means degree 2, cubic means degree 3, and quintic means degree 5.

You may see references to the order of a NURBS curve. The order of a NURBS curve is positive whole number equal to (degree+1). Consequently, the degree

is equal to order-1.

It is possible to increase the degree of a NURBS curve and not change its shape. It is not possible to reduce a NURBS curve’s degree without changing its


The control points are a list of at least (degree+1) points.

One of easiest ways to change the geometry of a NURBS curve is to move its control points. Rhino provides several ways to move control points. To perform

large free-form adjustments you simply use the mouse to drag the control point. Rhino provides other tools tailored for small precise adjustments.

The control points have an associated number called a weight. With a few exceptions, weights are positive numbers. When a curve’s control points all have

the same weight (usually 1), the curve is called non-rational, otherwise the curve is called rational. The R in NURBS stands for rational and indicates that a

NURBS curve has the possibility of being rational. In practice, most NURBS curves are non-rational. A few NURBS curves; circles and ellipses being notable

examples, are always rational. Rhino provides tools for examining and changing control point weights.

The knots are a list of degree+N-1 numbers, where N is the number of control points. Sometimes this list of numbers is called the knot vector. In this term, the

word vector does not mean 3 D direction.

This list of knot numbers must satisfy several technical conditions. The standard way to ensure that the technical conditions are satisfied is to require the numbers

to stay the same or get larger as you go down the list and to limit the number of duplicate values to no more than the degree. For example, for a degree 3

NURBS curve with 15 control points, the list of numbers 0,0,0,1,2,2,2,3,7,7,9,9,9 is a satisfactory list of knots. The list 0,0,0,1,2,2,2,2,7,7,9,9,9 is unacceptable

because there are four 2s and four is larger than the degree.

The number of times a knot value is duplicated is called the knot’s multiplicity. In the preceding example of a satisfactory list of knots, the knot value 0 has

multiplicity three, the knot value 1 has multiplicity one, the knot value 2 has multiplicity three, the knot value 7 has multiplicity two, and the knot value 9 has

multiplicity three. A knot value is said to be a full multiplicity knot if it is duplicated degree many times. In the example, the knot values 0, 2, and 9 have full

multiplicity. A knot value that appears only once is called a simple knot. In the example the knot values 1 and 3 are a simple knots.

If a list of knots starts with a full multiplicity knot, is followed by simple knots, terminates with a full multiplicity knot, and the values are equally spaced, then

the knots are called uniform. For example, if a degree 3 NURBS curve with 7 control points has knots 0,0,0,1,2,3,4,4,4, then the curve has uniform knots. The

knots 0,0,0,1,2,5,6,6,6 are not uniform. Knots that are not uniform are called non uniform. The NU in NURBS stands for non uniform and indicates that the

knots in a NURBS curve are permitted to be non-uniform.

Duplicate knot values in the middle of the knot list make a NURBS curve less smooth. At the extreme, a full multiplicity knot in the middle of the knot list

means there is a place on the NURBS curve that can be bent into a sharp kink. For this reason, some designers like to add and remove knots and then adjust

control points to make curves have smoother or kinkier shapes. Rhino has tools for removing and adding knots. Since the number of knots is equal to

(N+degree+1), where N is the number of control points, adding knots also adds control points and removing knots removes control points. Knots can be added

without changing the shape of a NURBS curve. In general, removing knots will change the shape of a curve. Rhino provides an advanced knot removing interface

that automatically performs appropriate knot removal when a user deletes a control point.

A common misconception is that each knot is paired with a control point. This is true only for degree 1 NURBS (polylines). For higher degree NURBS, there

are groups of 2 x degree knots that correspond to groups of degree+1 control points. For example, suppose we have a degree 3 NURBS with 7 control points

and knots 0,0,0,1,2,5,8,8,8. The first four control points are grouped with the first six knots. The second through fifth control points are grouped with the knots

0,0,1,2,5,8. The third through sixth control points are grouped with the knots 0,1,2,5,8,8. The last four control points are grouped with the last six knots.

Some modelers that use older algorithms for NURBS evaluation require two extra knot values for a total of degree+N+1 knots. When Rhino is exporting and

importing NURBS geometry, it automatically adds and removes these two superfluous knots as the situation requires.

The evaluation rule uses a mathematical formula that takes a number and assigns a point.

The formula involves the degree, control points, and knots. In the formula there are some things called B-spline basis functions. The BS in NURBS stands for

B-spline. The number the evaluation rule starts with is called a parameter. You can think of the evaluation rule as a black box that eats a parameter and produces

a point. The degree, knots, and control points determine how the black box works.

Rhino has evaluation tools. You can select a NURBS curve, type in the value of the parameter, and produce the corresponding point.

Conceptually, the knots determine the B spline basis functions. The values of the B spline basis functions at the parameter determine how the control points and

weights are averaged together to produce a point. Detailed discussions of the evaluation rule and B spline basis functions are available in many textbooks and

Web pages.

More details


Rhino crash course

2. år AAA, 20-09-2010

A short introduction to simple 2D geometry

in McNeels Rhinoceros 4.0.

Rhino 2D hvorfor ?

Alt den information der bliver givet her kan findes i de på rummet i

præsentation og udlagte tutorials s. 1-100.


- Viewports

- Commandline

- Status Bar

- Toolbar

- Layers (p. 40)

- Properties f3


Menu bar

Command history window

Command prompt

Layer menu


Grafics area

World axis icon

Viewport title

Main 1 and main 2 toolbars

Properties menu

Osnap toolbar

Status bar

Menus - Flyouts -

RHINO - Navigation (p.11, 20-26)

- Zoom, pan

- Mouse Wheel zoom

- Right mouse button pan, zoom

- Toolbar

RHINO - Import

- AutoCad drawing file ( dwg ) (Hør efter og skriv ned!!!)

- Pictures (Hør efter og skriv ned!!!)

RHINO - 2D line drawing (Tools simple)

- Line, polyline (p. 31)

- Rectangle, circle, ellipse ...(p.87)

- Selecting objekts (p.45)

RHINO - Transform (simple)(p.103-138)

- Move (p.115)

- Rotate (p.118)

- Trim - extent (p.127-130)

- Copy (p.117)

- scale (p.121)

RHINO - Øvelse 1

- Import jpg (pictureframe)

- Distance, scale

- Start drawing...(line, polyline...)

- Toolbar

RHINO - Import pictures

RHINO - Øvelse 2

- Import dwg files ( digitalt kort materiale fra sidste øvelse)

- Import Rhino fil fra øvelse 1

- Layers

- Transformation

RHINO - Import dwg

RHINO - Print og export

- Export dwg (Hør efter og skriv ned!!!)

- Export Illustrator (Hør efter og skriv ned!!!)

- Print pdf (p.235)

- SKALA...?


Z ZoomWindow

ZE ZoomExtents

zea zoomextentsall

zs zoomselected

zsa zoomselectedall


o Offset

p polyline

M Move

U ! _Undo

POn ! _PointsOn

POff ! _PointsOff

c copy

W Export

COn ‘_CurvatureGraph

COff ‘_CurvatureGraphOff

SL Section

l lines

TX _TextObject

g gcon

UG _Ungroup

sh shade

J join

ex extend

DI Distance

TR Trim

I Import

h hide

LA Layer

F Fillet

loff _OneLayerOff

sp split

es edgesrf

crva curvatureanalysis

AA Area

SC Scale

SCR ReadCommandFile

AR Array

cs interpcrvonsrf

et extrude

ct contour

SEC Contour

PE EditPtOn

PL Polyline

ia importcommandaliases

ih ! Invert Hide

cu ! interpcrv

PO Point

SET Options

SHA Shade

POL Polygon

d ! distance

ii import

pr project

db ! dupborder

ilk invert lock

REC Rectangle

REG PlanarSrf

EXT Extrude

in intersect

dd ! layer

iv ReadNamedViewsFromFile

BR Split

de dupedge

REV Revolve

RO Rotate

k matchlayer

HI Make2D

lf loft

lk lock

CH Properties

CHA Chamfer

ln layeron

lna alllayerson

IMP Import

lo layeroff

loa lo *

co contour

ly layer

m2n meshtonurb

cp properties

nmo SetObjectNameMultiple

no setobjectname

oe onelayeron

of onelayeroff

ol onelayeroff

on onelayeron

ow openworkspace

pa patch

pct placecameratarget

pn pton

rb rebuild

rbs rebuildsrf

s1 sweep1

s2 sweep2

s3 srfpt

sc1 scale1

se section

sil silhouette

sla selall

slc selcrv

sll sellayer

LEN ExtendByLine

mi mirror

ca curvatureanalysis

cg curvatureGraphOn

cgo curvatureGraphoff

ci circle

da dimaligned

dt detachtrim

e delete

ea exportcommandaliases

eb endbulge

ec ExtendCrvOnSrf

ei extractisoparm

ep editpton

ew extractwireframe

exc ExtrudeAlongCrv

exs export

fa fair

fs filletsrf

je JoinEdge

li what CommandHistory

MA Properties

ml matchlayer

ms matchsrf

op options

os offsetsrf

r rotate

re renderpreview

si SplitSrf

sln selname

slp selpolyline

sls selsrf selpolysrf

sm smooth

SN SnapOptions

spc simplifycrv

ss showselected

sts shrinktrimmedsrf

sw saveworkspaceas

sw1 sweep1

sw2 sweep2

sx split

t trim

x explode

rc restorecplane

ut untrim

to toolbar

ll linev

xs extractsrf

pm perspectivematch

esr ExtrudeSrf

pi pipe

ri ribbon

rw removewallpaper

ics InterpCrvOnSrf

RR Render

oce OrientCrvToEdge

fl Flow

opc OrientPerpToCrv

scp savecplane

2d make2d

a arc3pt

al orient

cl changelayer

cr curve

il invert lock

DIV Divide

sr planarsrf

ED EditText

LS What

EL Ellipse

ME Measure

exp explode

tg ! placecameratarget enter

tt ! top ze

u3 CPlane3Pt

SPLINE InterpCrv

ul all unlock invert

SPL InterpCrv

ORBIT RotateView

uls unlockselected

urs unrollsrf

SU BooleanDifference

vl lineV

vr restoreview

vs ! saveview

TOR Torus

wf front ww

wr right ww

ww export

RPR RenderOptions

UNI BooleanUnion

V RestoreView

VP PlaceCameraTarget

xt extrude

zd zoomdynamic

3A Array

3DO RotateView

3F Plane

3P Polyline

ng setgroupname

slg selgroup

gr group

ws _Worksession







Byfunktioner 100%

Bebyggelsesprocent 300%



2D Line drawing

2D Transformation

3D Extrusion

3D Transformation






-> FRI

-> MAX 11 M

Precision modeling (p.49)

Absolute Coordinates

Relative Coordinates

Distance Constraint Entry

Modeling with Solids (p.165)

Solid Tools (p.165)

Extrude Crv (p.166)

Cut by lines


Extrude Crv



Rhino 3D Øvelse_01





-> FRI

-> MAX 11 M

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