A Definitive Resource for Geometry Constrainment

8/17/2019 A Definitive Resource for Geometry Constrainment

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A Definitive Resource for

Geometry Constrainment

from: Additional Drawing

Considerations and ConventionalPractices


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Geometric Definitions

Ways to Define and Construct geometry for:

• Points

•

Lines• Circles

• Planes


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Defining Points:

1a. By coordinates

(rectangular)


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Defining Points:

1b. By coordinates (polar)


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Defining Points:

2. as the intersection of 2

lines:


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Defining Points:

3. as the intersection of a

line and a circle (multiplesolutions)


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Defining Points:

4. at the intersection of 2

circles (multiple solutions)


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Defining Points:

5. on a circle at an angle

to the XAXIS


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Defining Points:

6. at the center of a circle


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Defining Points:

7. at the intersection of

three planes


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Defining Points:

8. by the location in a pattern/array/table


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Defining a Line:

1. through two points


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Defining a Line:

2. through a point and

tangent to a circle


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Defining a Line:

3. tangent to two circles


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Defining a Line:

4. as the X- or Y-axis

BTW, SLN ≡ Symbolic Line


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Defining a Line:


ATANGL with a given line


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Defining a Line:


PARLEL to a given line


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Defining a Line:

7. through a point an

PERPTO a given line


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Defining a Line:

8. PARLEL to a given line

and OFFSET a given

distance


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Defining a Line:

9. intersection of two

planes


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Defining Planes:

1. by the coefficients of the equation:

ax + by + cz – d = 0

2. as passing through 3 points

3. passing through a point and PARLEL to a

given plane

4. PARLEL to a given plane at a distance

5. passing through a point and PERPTO a vector


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Defining Planes:

1. by the coefficients of

the equation:

ax + by + cz – d = 0


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Defining Planes:

2. as passing through 3

points


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Defining Planes:

3. passing through a point

and PARALLEL to a given

plane


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Defining Planes:

4. PARLEL to a given

plane at a distance


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Defining Planes:

5. passing through a

point and PERPTO a

vector


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Defining Planes:

6. passing through 2 points and PERPTO a given

plane

7. passing through 1 point and PERPTO two

intersecting planes


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Defining Planes:

6. passing through 2 points and PERPTO a givenplane


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Defining Planes:

7. passing through 1 point and PERPTO two

Intersecting planes


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Defining Circles:

1. by a center point and radius

2. by the center and a line to which it is Tangent3. by the center and point on the Circumference

4. by three points on the Circumference

5. by a center point and Tangent to a givencircle (multiple solutions)


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Defining Circles:

1. by a center point

and radius


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Defining Circles:

2. by the center point

and a line to which it is

Tangent


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Defining Circles:

3. by the center and

point on the

Circumference


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Defining Circles:

4. by three points on

the Circumference


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Defining Circles:

5. by a center point and

Tangent to a given circle

(multiple solutions)


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Defining Circles:

6. by a Radius and Tangent to Two intersectingLines (multiple solutions)

7. with a given Radius Tangent to a Line andPassing through a Point (multiple solutions)

8. by a Radius and Tangent to a Line and a Circle

(multiple solutions)9. by a radius and Tangent to 2 Circles (multiple

solutions)


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Defining Circles:

8. by a Radius, and

Tangent to a Line and a

Circle (multiple solutions)


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Defining Circles:

9. by a radius and

Tangent to 2 Circles

(multiple solutions)


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Additional Drawing ConsiderationsGeometric Construction

Constructing points of tangency:

• line from a point tangent to an arc

• arc tangent to two (skew) lines

• arc tangent to Perpendicular lines

• arc tangent to an arc and a line

•arc tangent to two arcs

Earle, p.95-97; blackboard

presentation. Sorry, no slides

or time to present this


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Additional Drawing ConsiderationsConic Sections

• parabola• hyperbola

• ellipse

circle• other quadric surfaces

• parabolic /hyperbolic/elliptic cylinder

• real ellipsoid

•

hyperboloid (one sheet/two sheets)• elliptic paraboloid

• hyperbolic paraboloid


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Additional Drawing ConsiderationsConic Sections

• parabola

• hyperbola

• ellipse


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Additional Drawing ConsiderationsQuadric Surfaces


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there is a separate presentation on airfoil basics


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A Definitive Resource for

Geometry Constrainmentfrom: Additional Drawing

Considerations and Conventional

Practices

end of presentation

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A Definitive Resource for Geometry Constrainment

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