a definitive resource for geometry constrainment
TRANSCRIPT
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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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Geometric Definitions
Defining Points:
1a. By coordinates
(rectangular)
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Geometric Definitions
Defining Points:
1b. By coordinates (polar)
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Geometric Definitions
Defining Points:
2. as the intersection of 2
lines:
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Geometric Definitions
Defining Points:
3. as the intersection of a
line and a circle (multiplesolutions)
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Geometric Definitions
Defining Points:
4. at the intersection of 2
circles (multiple solutions)
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Geometric Definitions
Defining Points:
5. on a circle at an angle
to the XAXIS
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Geometric Definitions
Defining Points:
6. at the center of a circle
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Geometric Definitions
Defining Points:
7. at the intersection of
three planes
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Geometric Definitions
Defining Points:
8. by the location in a pattern/array/table
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Geometric Definitions
Defining a Line:
1. through two points
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Geometric Definitions
Defining a Line:
2. through a point and
tangent to a circle
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Geometric Definitions
Defining a Line:
3. tangent to two circles
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Geometric Definitions
Defining a Line:
4. as the X- or Y-axis
BTW, SLN ≡ Symbolic Line
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Geometric Definitions
Defining a Line:
5. through a point and
ATANGL with a given line
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Geometric Definitions
Defining a Line:
6. through a point and
PARLEL to a given line
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Geometric Definitions
Defining a Line:
7. through a point an
PERPTO a given line
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Geometric Definitions
Defining a Line:
8. PARLEL to a given line
and OFFSET a given
distance
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Geometric Definitions
Defining a Line:
9. intersection of two
planes
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Geometric Definitions
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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Geometric Definitions
Defining Planes:
1. by the coefficients of
the equation:
ax + by + cz – d = 0
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Geometric Definitions
Defining Planes:
2. as passing through 3
points
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Geometric Definitions
Defining Planes:
3. passing through a point
and PARALLEL to a given
plane
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Geometric Definitions
Defining Planes:
4. PARLEL to a given
plane at a distance
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Geometric Definitions
Defining Planes:
5. passing through a
point and PERPTO a
vector
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Geometric Definitions
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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Geometric Definitions
Defining Planes:
6. passing through 2 points and PERPTO a givenplane
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Geometric Definitions
Defining Planes:
7. passing through 1 point and PERPTO two
Intersecting planes
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Geometric Definitions
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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Geometric Definitions
Defining Circles:
1. by a center point
and radius
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Geometric Definitions
Defining Circles:
2. by the center point
and a line to which it is
Tangent
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Geometric Definitions
Defining Circles:
3. by the center and
point on the
Circumference
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Geometric Definitions
Defining Circles:
4. by three points on
the Circumference
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Geometric Definitions
Defining Circles:
5. by a center point and
Tangent to a given circle
(multiple solutions)
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Geometric Definitions
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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Geometric Definitions
Defining Circles:
8. by a Radius, and
Tangent to a Line and a
Circle (multiple solutions)
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Geometric Definitions
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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Additional Drawing ConsiderationsQuadric Surfaces
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Additional Drawing ConsiderationsQuadric Surfaces
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