Geometric Construction - Engineering Graphics - Lecture Slides, Slides of Computer Graphics and Animation

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Geometric Construction

Objective

• To review basic terminology and concepts

related to geometric forms

• To present the use of several geometric

tools/methods which help in the

understanding and creation of engineering

drawings

Coordinate Systems

• Origin (reference point)
• 2-Dimensional Coordinate System
  • Cartesian (x,y)
  • Polar (r,θ)
• 3-Dimensional Coordinate System
  • Cartesian (x,y,z)
  • Cylindrical (z,r,θ)
  • Spherical (r,θ,φ)

Cartesian Coordinate System

• Defined by two/three mutually perpendicular axes which intersect at a common point called the origin - x-axis - horizontal axis - positive to the right of the origin as shown - y-axis - vertical axis - positive above the origin as shown - z-axis (added for a 3-D coordinate system) - normal to the xy plane - positive in front of the origin as shown

Polar Coordinate System

• The distance from the origin to the point in the xy plane is specified as the radius (r)
• The angle measured form the positive x axis is specified as θ
• Positive angles are defined according to the right hand rule
• Conversion between Cartesian and polar
  • x=rcos θ , y=rsin θ
  • x^2+y^2=r^2 , θ=tan -1^ (y/x)

Cylindrical Coordinate System

• Same as polar except a z-axis is added which is normal to the xy plane in which angle θ is measured
• The direction of the positive z-axis is defined by the right hand rule
• Useful for describing cylindrical features

Redefining Coordinates

• Absolute coordinates
  • measured relative to the origin
  • LINE (1,2,1) - (4,4,7)
• Relative coordinates
  • measured relative to a previously specified point
  • LINE (1,2,1) - @(3,2,6)
• World Coordinate System
  • a stationary reference
• User Coordinate System (ucs)
  • change the location of the origin
  • change the orientation of axes

Geometric Elements

• A point
• A line
• A curve
• Planes
• Closed 2-D elements
• Surfaces
• Solids

A Line

• Has length and direction but no width
• All points are collinear
• May be infinite
  • At least one point must be specified
  • Direction may be specified with a second point or with an angle
• May be finite
  • Defined by two end points
  • Defined by one end point, a length, and direction Docsity.com

A Curve

• The locus of points along a curve are not

collinear

• The direction is constantly changing
• Single curved lines
  • all points on the curve lie on a single plane
• A regular curve
  • The distance from a fixed point to any point on the curve is a constant
  • Examples: arc and circle

Closed 2-D Elements (planar)

• Triangles
  • Three sides
  • Equilateral triangle (all sides equal, 60 deg. angles)
  • Isosceles triangle (two sides equal)
  • Right triangle (one angle is 90 degrees)
    • A^2+B^2=C^2 (Pythagorean theorem)
    • Sinθ=A/C
    • Cosθ=B/C (^) B

A

C θ

Closed 2-D Elements (planar)

• Circles
  • Radius (R)
  • Diameter (D)
  • Angle (1 rev = 360 o^ 0’ 0”)
  • Circumference (23.14159R)
  • Tangent
  • Chord
    • A line perpendicular to the midpoint of a chord passes through the center of the circle
  • Concentric circles

D

R θ

Surfaces

• Does not have thickness
• Two dimensional at every point
  • No mass
  • No volume
• May be planar
• May be used to define the boundary of a

3-D object

Solids

• Three dimensional
• They have a volume
• Regular polyhedra
  • Have regular polygons for faces
  • All faces are the same
    • Prisms
      • Two equal parallel faces
      • Sides are parallelograms
    • Pyramids
      • Common intersection point (vertex)
    • Cones
    • Cylinders
    • Spheres