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Слайды и текст к этой презентации:
№1 слайд
Содержание слайда: Week 4: Geometric Modeling – Parametric Representation of Analytic Curves
Spring 2018, AUA
№2 слайд
Содержание слайда: Intro to Geometric Modeling (GM)
№3 слайд
Содержание слайда: Objects of Representation
№4 слайд
Содержание слайда: Types of Representation
№5 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
№6 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
Can be extended to higher objects. (4th parameter )
№7 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
Can be extended to higher objects. (4th parameter )
More DOF for controlling curves and surfaces.
№8 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
Can be extended to higher objects. (4th parameter )
More DOF for controlling curves and surfaces.
Transformations (distinct separation between shape and trans. info).
№9 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
Can be extended to higher objects. (4th parameter )
More DOF for controlling curves and surfaces.
Transformations (distinct separation between shape and trans. info).
Vector – matrix multiplication (not good for you, good for comp).
№10 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
Can be extended to higher objects. (4th parameter )
More DOF for controlling curves and surfaces.
Transformations (distinct separation between shape and trans. info).
Vector – matrix multiplication (not good for you, good for comp.).
Bounded objects are represented with one-to one relationship.
№11 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
Can be extended to higher objects. (4th parameter )
More DOF for controlling curves and surfaces.
Transformations (distinct separation between shape and trans. info).
Vector – matrix multiplication (not good for you, good for comp.).
Bounded objects are represented with one-to one relationship.
No problems for slope calculation.
№12 слайд
Содержание слайда: Advantages of PR
Get rid of dependency of the coordinates (X, Y, Z) from each other.
Can be extended to higher objects. (4th parameter )
More DOF for controlling curves and surfaces.
Transformations (distinct separation between shape and trans. info).
Vector – matrix multiplication (not good for you, good for comp.).
Bounded objects are represented with one-to one relationship.
No problems for slope calculation.
Discretizing entities
№13 слайд
Содержание слайда: Parametric Representation (PR)
X = f(t)
Y = g(t)
Z = h(t)
№14 слайд
Содержание слайда: PR of 3D Curve
№15 слайд
Содержание слайда: PR of Analytic Curves
Analytic curves are defined by analytic equations
№16 слайд
Содержание слайда: Lines: 2 points
№17 слайд
Содержание слайда: Lines: point and direction
№18 слайд
Содержание слайда: Parametric equation from NP Implicit Equation: Example
№19 слайд
Содержание слайда: Circles
№20 слайд
Содержание слайда: Ellipses
№21 слайд
Содержание слайда: Examples
Find the equation and endpoints of a line that passes through point P1, parallel to an existing line, and is trimmed by point P2.
Relate the following CAD commands to their mathematical foundations:
The command to measure the angle between two intersecting lines.
The command to find the distance between a point and a line.