Index

arc length

arc length parametrization

artificial singularity

3.1

auxiliary variable method

4.5

Bézier curve

algorithms: 1.3.5
derivative: 1.3.4
properties: 1.3.4

Bézier point

1.3.4

Bézier surface

1.3.6

B-spline basis function

1.4.1

derivative: 1.4.1

B-spline curve

algorithms: 1.4.3
derivative: 1.4.2
properties: 1.4.2

B-spline surface

1.4.4

basis conversion

B-spline to Bézier

monomial to Bernstein

one variable: 4.4
two variables: 4.4

Bernstein polynomial

derivative: 1.3.1
arithmetic operation: 1.3.2
properties: 1.3.1

binormal vector

Boehm's algorithm

1.4.3

border point

5.8.1.3

Boundary Representation

boundary value problem

finite difference method: 10.3.3
relaxation method: 10.3.3
shooting method: 10.3.2

bounding box

5.4.2.2 | 5.4.2.2

bounding wedge

5.6.2

calculus of variations

10.2.1

Christoffel symbols

10.2.1

clamped curves

clamped knots

class of function

1.1.1 | 1.2

collinear normal point

5.8.2.3 | 7.2.2

condition number of root

1.3.3

conic sections

conjugate point

10.1

Constructive Solid Geometry

continuity

geometric: 1.3.5
parametric: 1.3.5

contouring

8.1.1.2 | 8.5.3

control net

1.3.6

control polygon

1.3.4

convex hull

1.3.4

convex hull property

1.3.4 | 1.4.2

curvature

tangential intersection point: 6.4.2
transversal intersection curve: 6.3.2

curvature map

8.1.3.4

curvature plots

8.1.3.1

curvature vector

cusp

8.2.3

cyclide

9.1 | 11.1.1

Darboux vector

8.1.5.2

de Boor algorithm

1.4.3

de Boor points

de Casteljau algorithm

1.3.5 | 4.4

degenerate patch

1.3.6

denormalized number

4.8.1

developable surface

8.1 | 9.7.1 | 11.4.2

development

10.8

directrix

distance function

7.1

stationary points: 7.3.1

Dupin's cyclide patch

9.1

Dupin's indicatrix

3.6 | 6.4.1

ellipsoid

1.2 | 1.2

elliptic cone

1.2 | 1.2 | 3.1

elliptic cylinder

1.2 | 1.2

elliptic paraboloid

umbilic: 8.3

elliptic point

end point geometric property

1.3.4 | 1.4.2

essential singularity

3.1

Euler's equation

10.2.1

Euler's theorem

3.6 | 9.7.1

evolute

8.1.3.5

explicit curve

explicit quadratic surface

8.3

exponent

4.6

first fundamental form

3.2

coefficients: 3.2

flat point

3.3 | 3.4

floating point arithmetic

4.6 | 4.8.1

focal curve

8.1.3.5 | 8.1.3.5

focal surface

8.1.3.5 | 8.1.3.5

Folium of Descartes

Frenet-Serret formulae

2.4 | 2.4 | 6.2 | 11.2.1

Gaussian curvature

3.4 | 3.5

ellipsoid: 3.5.2
elliptic cone: 3.5.2
explicit surface: 3.5.1
hyperbolic cylinder: 3.5.2
implicit surface: 3.5.2

generator

geodesic

8.1.3.8 | 10. | 10.1

curvature: 8.1.3.8 | 10.2.1
curvature vector: 3.3 | 10.2.1
equation of: 10.2.1 | 10.2.2
offset: 10.7
on developable surface: 10.8

geometry invariance property

1.3.4 | 1.4.2

Gröbner bases

4.3.1

Greville abscissa

1.4.1

helix

highlight line

8.1.2.4

hodograph

1.3.4 | 5.6.2

hyperbolic cylinder

hyperbolic paraboloid

1.2 | 3.2 | 3.5.1 | 10.2.1

hyperbolic point

hyperboloid of one sheet

hyperboloid of revolution

hyperboloid of two sheets

IGES

1.5

implicit curve

implicit surface

implicitization

5.4.2.4 | 5.4.2.4

incidence intransitivity

5.3

inflection line

inflection point

2.2 | 8.1.3.1 | 8.1.3.4 | 8.1.3.6

initial value problem

10.3.1

interrogation

first-order: 8.1.2.1
fourth-order: 8.1.5
second-order: 8.1.3
third-order: 8.1.4.1
zeroth-order: 8.1.1

intersection

curve to curve: 5.6
curve to surface: 5.7
lattice method: 5.8.2.1
marching method: 5.8.2.3
point to curve: 5.4
point to point: 5.3
point to surface: 5.5
subdivision method: 5.8.2.2
surface to surface: 5.8

interval arithmetic

4.6 | no title

algebraic properties: 4.7
rounded interval arithmetic: 4.8

interval Newton's method

4.7

Interval Projected Polyhedron (IPP) algorithm

4.9

intrinsic equation

2.4

inverse function theorem

9.3

inversion

isophotes

knot insertion

knot removal

knot vector

clamped: 1.4.2

Lagrange multiplier

8.4

line of curvature

3.4 | 8.1.3.7 | 9.1

linear precision

1.3.1 | 4.4

linkage curve theorem

8.1.3.5

local support property

mantissa

4.6 | 4.8.1

marching method

7.3.2

maximum principal curvature

ellipsoid: 3.5.2
elliptic cone: 3.5.2
hyperbolic cylinder: 3.5.2

mean curvature

3.4 | 3.5

ellipsoid: 3.5.2
elliptic cone: 3.5.2
explicit surface: 3.5.1
hyperbolic cylinder: 3.5.2
implicit surface: 3.5.2

medial axis

11.1.3

meridians

Meusnier's theorem

minimum principal curvature

ellipsoid: 3.5.2
elliptic cone: 3.5.2
hyperbolic cylinder: 3.5.2

Monge form

3.5.1 | 9.2

NC machining

11.1.2

Newton's method

modified: 4.2
n variables: 10.3.3
one variable: 4.1 | 4.2

node

1.4.1

non-algebraic distance

5.4.1

non-arc-length parametrization

Non-Uniform Rational B-Spline (NURBS)

1.5

curve: 1.5
surface: 1.5

nonparametric form

normal curvature vector

normal plane

6.3.4

normal pyramid

11.3.5

normal vector

curve: 2.2
surface: 3.1

normalized number

4.8.1

offset curve

11.2

approximation: 11.2.4
cusp: 11.2.3
extraordinary point: 11.2.2
irregular point: 11.2.2
isolated point: 11.2.3
ordinary cusp: 11.2.2
self-intersection: 11.2.2 | 11.2.3
singularity: 11.2.2

offset surface

11.3

approximation

11.3.7

Gaussian curvature

implicit surface

irregular point

mean curvature

principal curvature

11.3.1

self-intersection

11.3.2

explicit quadratic surface: 11.3.4
implicit quadratic surface: 11.3.3
parametric surface: 11.3.5
tracing: 11.3.6

singularity

11.3.2

ordinary point

2.1 | 3.1

orthotomics

8.1.3.6

osculating plane

Oslo algorithm

1.4.3

overlapping

5.9

parabolic cylinder

parabolic point

paraboloid of revolution

parallels

parametric curve

parametric speed

parametric surface

pick feed

11.1.2

pipe surface

11.6

planar point

3.3 | 3.4

polynomial solver

algebraic technique: 4.3.1
balanced system: 4.4
homotopy method: 4.3.2
hybrid technique: 4.3.1
overconstrained system: 4.4
subdivision method: 4.3.3
underconstrained system: 4.4

principal direction

principal normal vector

principal patch

9.1

procedural curve

procedural surface

Projected Polyhedron (PP) algorithm

4.4

Pythagorean hodograph

11.4

quadric

1.2 | 3.5.2

radial curve

8.1.3.3

radius of curvature

rational arithmetic

4.6

rational number

5.2.3

ray tracing

8.1.2.1

rectifying plane

reflection line

8.1.2.3

regular point

on curve: 2.1
on surface: 3.1

resultant

4.3.1 | 5.4.2.4

root mean square curvature

8.1.3.4

rotation matrix

9.3

ruled surface

conical: 5.5.2.1
cylindrical: 5.5.2.1

ruling

secant method

10.5

second fundamental form

coefficients: 3.3

self-intersection

5.10 | 5.10

semi-cubical parabola

shaded image

8.1.2.1

shooting method

10.3.1

significant digits

4.6

singly curved surface

singular point

2.1 | 3.1 | 5.8.1.3

span

STEP

1.5

surface inflection

surface of revolution

3.4 | 5.5.2.1

tangent plane

3.1

tensor product surface

1.3.6 | 1.4.4

tolerance region

11.1.4

tool driving plane

11.1.2

torsion

2.3 | 6.2 | 8.1.4.1

transversal intersection curve: 6.3.3

torus

1.5 | 5.5.2.1

total curvature

8.1.5.2

trip algorithm

8.5.3

triple scalar product

turning point

5.8.1.3

umbilic

3.4 | 8.2.3 | 9.1 | 9.1

criterion: 9.5
generic: 9.2
index: 9.2
lemon pattern: 9.2
lemon type: 8.3
monstar pattern: 9.2
non-generic: 9.2
star pattern: 9.2

unit in the last place (ulp)

4.8

unit speed

unit tangent vector