Darstellende Geometrie/3D-Geometry

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  • 1 Fundamental Terms of Geometry
    • 1.1 Systems of Coordinates
      • 1.1.0
        Systems of Coordinates
        1.1.0
        Theory on CD
      • 1.1.1
        Example: Define Cartesian Coordinates
        1.1.1
        Example on CD | Worksheet on CD
      • 1.1.2
        Example: Polar Coordinates
        1.1.2
        Example (ppsx) | Worksheet (pdf)
      • 1.1.3
        Example: Cylindrical Coordinates
        1.1.3
        Example (ppsx) | Worksheet (pdf)
      • 1.1.4
        Example: Spherical Coordinates
        1.1.4
        Example (ppsx) | Worksheet (pdf)
    • 1.2 Main Solids: Prism, Pyramid, Cone and Cylinder
      • 1.2.1
        Definition of Prism und Cylinder
        1.2.1
        Theory on CD | Worksheet (pdf)
      • 1.2.2
        Definition of Pyramid and Cone
        1.2.2
        Theory on CD | Worksheet (pdf)
      • 1.2.3
        Platonic and Archimedic Solids
        1.2.3
        Theory (ppsx) | Worksheet (pdf)
      • 1.2.4
        Rotational Surfaces
        1.2.4
        Theory (ppsx) | Worksheet (pdf)
      • 1.2.5
        Contour and Apparent Contour
        1.2.5
        Theory (ppsx) | Worksheet (pdf)
    • 1.3 Analyse Objects by Main Solids and Surfaces
  • 2 Types of Projections
    • 2.1 Types of Projections and Properties
      • 2.1.0
        Types of Projection
        2.1.0
        Theory on CD
      • 2.1.1
        Properties of Parallel Projection
        2.1.1
        Theory on CD
      • 2.1.2
        Properties of Central Projection
        2.1.2
        Theory on CD
    • 2.2 Axonometry
      • 2.2.0
        Axonometric Views
        2.2.0
        Theory on CD
      • 2.2.1
        Example: Different Axonometric Views of a Solid
        2.2.1
        Example on CD | Worksheet on CD
      • 2.2.2
        Example 1: Axonometric Views
        2.2.2
        Example (ppsx) | Worksheet (pdf)
      • 2.2.3
        Example 2: Axonometric Views
        2.2.3
        Example (ppsx) | Worksheet (pdf)
    • 2.3 Principle Views
      • 2.3.0
        Introduction of Principle Views
        2.3.0
        Theory on CD
      • 2.3.1
        Example 1: Axonometric View to Principle Views
        2.3.1
        Example on CD | Worksheet on CD
      • 2.3.2
        Example 2: Axonometric View to Principle Views
        2.3.2
        Example on CD | Worksheet on CD
      • 2.3.3
        Example 3: Axonometric View to Principle Views
        2.3.3
        Example on CD | Worksheet on CD
      • 2.3.4
        Example 4: Principle Views to Axonometric View
        2.3.4
        Example on CD | Worksheet on CD
      • 2.3.5
        Example A,B: Completing Principle Views
        2.3.5
        Example on CD | Worksheet  A-D on CD
        2.3.5
        Example C,D: Completing Principle Views
        2.3.5
        Example on CD
        2.3.5
        Example E,F: Completing Principle Views
        2.3.5
        Example (ppsx) | Worksheet E-H (pdf)
        2.3.5
        Example G,H: Completing Principle Views
        2.3.5
        Example (ppsx)
      • 2.3.6
        Example A,B: Define Profile View
        2.3.6
        Example (ppsx) | Worksheet (pdf)
        2.3.6
        Example C,D: Define Profile View
        2.3.6
        Example (ppsx)
      • 2.3.7
        Example A,B: Define Plan View
        2.3.7
        Example (ppsx) | Worksheet (pdf)
        2.3.7
        Example C,D: Define Plan View
        2.3.7
        Example (ppsx)
    • 2.4 Additional Auxiliary View
      • 2.4.0
        Introduction of an Auxiliary View
        2.4.0
        Theory on CD
  • 3 Spatial Operations
    • 3.1 Fundamental Spatial Transformations
      • 3.1.0
        Fundamental Spatial Transformations
        3.1.0
        Theory on CD
      • 3.1.1
        Example: Reflection about a Plane
        3.1.1
        Example a-h on CD | Worksheet a-h on CD | Example i-l (ppsx) | Worksheet i-l (pdf)
      • 3.1.2
        Example: Rotation about an Axis
        3.1.2
        Example a-h on CD | Worksheet a-h on CD | Example i-k (ppsx) | Worksheet i-k (pdf)
      • 3.1.3
        Example: Spot Rotation
        3.1.3
        Example on CD | Worksheet on CD
    • 3.2 Advanced Spatial Transformations
      • 3.2.0
        Advanced Spatial Transformations
        3.2.0
        Theory on CD
    • 3.3 Boolean Operations
      • 3.3.0
        Boolean Operations
        3.3.0
        Theory on CD
      • 3.3.1
        Example: Boolean Operations
        3.3.1
        Example on CD | Worksheet on CD
      • 3.3.2
        Example: Boolean Operations 2
        3.3.2
        Example (ppsx) | Worksheet (pdf)
  • 4 Constructions in Axonometry
    • 4.1 Intercept and Intersection Line with an Image Plane
      • 4.1.0
        Intercept of a Straight Line with an Image Plane
        4.1.0
        Theory on CD
      • 4.1.1
        Example A,B,C: Intercepts of Line with Image Planes
        4.1.1
        Example on CD | Worksheet on CD
        4.1.1
        Example D,E,F: Intercepts of Line with Image Planes
        4.1.1
        Example on CD
      • 4.1.2
        Intersection Lines and Principle Lines of a Plane
        4.1.2
        Theory on CD
      • 4.1.3
        Example: Intersection Lines of a Plane with Image Planes
        4.1.3
        Example on CD | Worksheet on CD
    • 4.2 Intersection of Cube and Plane
      • 4.2.0
        Intercept and Intersection Line
        4.2.0
        Theory on CD
      • 4.2.1
        Example 1- A,B,C: Cube Cut By Plane
        4.2.1
        Example on CD | Worksheet on CD
        4.2.1
        Example 1- D,E: Cube Cut By Plane
        4.2.1
        Example on CD
        4.2.1
        Example 1- F,G,H: Cube Cut By Plane
        4.2.1
        Example on CD
      • 4.2.2
        Example 2 - A,B: Cube Cut By Plane
        4.2.2
        Example on CD | Worksheet on CD
        4.2.2
        Example 2 - C,D: Cube Cut By Plane
        4.2.2
        Example on CD
    • 4.3 Plain Solid Cut by Plane
      • 4.3.1
        Example 1: Solid Cut by Plane
        4.3.1
        Example on CD | Worksheet on CD
      • 4.3.2
        Example 2: Letter S and Number 2 Cut by Plane
        4.3.2
        Example on CD | Worksheet on CD
      • 4.3.3
        Example 3: Solid Cut by Plane
        4.3.3
        Example on CD | Worksheet on CD
      • 4.3.4
        Example 4: Technical Solid Cut by Plane
        4.3.4
        Example on CD | Worksheet on CD
      • 4.3.5
        Example 5: Letter H and Letter M Cut by Plane
        4.3.5
        Example on CD | Worksheet on CD
    • 4.4 Intersection of Lines and Planes
      • 4.4.0
        Intercept of a Straight Line with any Plane
        4.4.0
        Theory on CD
      • 4.4.1
        Example: Intercept of Straight Line AB with a Plane (scaffold of a Cube)
        4.4.1
        Example on CD | Worksheet on CD
      • 4.4.2
        Example: Intersection Line of Two Planes
        4.4.2
        Example on CD | Worksheet on CD
      • 4.4.3
        Example: Intersection of Triangle and Parallelogram
        4.4.3
        Example (ppsx) | Worksheet (pdf)
      • 4.4.4
        Example: Intersection Line of Two Triangles
        4.4.4
        Example (ppsx) | Worksheet (pdf)
    • 4.5 Intersection of Pyramid and Prism
      • 4.5.1
        Example: Truncated Pyramid Cut by Prism
        4.5.1
        Example (ppsx) | Worksheet (pdf)
      • 4.5.2
        Example: Truncated Hexagonal Pyramid with Cuboid
        4.5.2
        Example (ppsx) | Worksheet (pdf)
  • 5 Constructions in Principle Views
    • 5.1 Special Position of a Line and a Plane
      • 5.1.0
        Principle Lines
        5.1.0
        Theory on CD
      • 5.1.1
        Principle Planes
        5.1.1
        Theory on CD
      • 5.1.2
        Line Appearing as a Point - Point View of a Line
        5.1.2
        Theory on CD
      • 5.1.3
        Plane Appearing as an Edge- Edge View of a Plane
        5.1.3
        Theory on CD
      • 5.1.4
        Example: Transfer Points by Coordinates into Principle Views
        5.1.4
        Example (ppsx) | Worksheet (pdf)
      • 5.1.5
        Example: Name Special Position of Spatial Lines
        5.1.5
        Example (ppsx) | Worksheet (pdf)
      • 5.1.6
        Example: Name Special Position of Planes
        5.1.6
        Example (ppsx) | Worksheet (pdf)
    • 5.2 True Length of a Segment
      • 5.2.0
        True Length of a Segment - Trapezoid
        5.2.0
        Theory on CD | Worksheet on CD
        5.2.0
        True Length of a Segment - Triangle of Difference
        5.2.0
        Theory on CD
        5.2.0
        True Length of a Segment - Auxiliary View
        5.2.0
        Theory on CD
      • 5.2.1
        Example A,B: True Length of a Segment - Triangle of Difference
        5.2.1
        Example on CD | Worksheet A,B on CD
        5.2.1
        Example C,D: True Length of a Segment - Triangle of Difference
        5.2.1
        Example (ppsx) | Worksheet C,D (pdf)
      • 5.2.2
        Example A,B: Transfer Distance on a Line
        5.2.2
        Example on CD | Worksheet A,B on CD
        5.2.2
        Example C,D: Transfer Distance on a Line
        5.2.2
        Example (ppsx) | Worksheet C,D (pdf)
    • 5.3 Project a Line as a Point and a Plane as an Edge
      • 5.3.0
        Project a Line as a Point - Two Auxiliary Views
        5.3.0
        Theory on CD | Worksheet on CD
      • 5.3.1
        Project a Plane as an Edge - Auxiliary View
        5.3.1
        Theory on CD | Worksheet on CD
    • 5.4 Locating Points in a Plane
      • 5.4.0
        Locate a Point in a Plane - Auxiliary Line
        5.4.0
        Theory on CD
      • 5.4.1
        Example: Locate Points in the Plane ABC
        5.4.1
        Example on CD | Worksheet on CD
      • 5.4.2
        Locate a Point in a Plane - Principle Line
        5.4.2
        Theory on CD
      • 5.4.3
        Example: Locate Points - Use Principle Lines
        5.4.3
        Example on CD | Worksheet on CD
      • 5.4.4
        Example A: Intersection of a Prism and a Plane - Locate Points
        5.4.4
        Example on CD | Worksheet on CD
        5.4.4
        Example B: Intersection of a Prism and a Plane - Locate Points
        5.4.4
        Example on CD
    • 5.5 Spatial Position of Lines to Each Other
      • 5.5.0
        Position of Two Lines to Each Other in Space
        5.5.0
        Theory on CD | Worksheet on CD
    • 5.6 True Size and Shape of Planar Figure
      • 5.6.0
        Example: True Shape of a Planar Figure - Two Auxiliary Views
        5.6.0
        Example (ppsx) | Worksheet (pdf)
      • 5.6.1
        Example: True Shape of a Planar Figure - Auxiliary View and Rotation
        5.6.1
        Example (ppsx) | Worksheet (pdf)
      • 5.6.2
        Example: True Shape of Planar Figure - Revolution of a Plane
        5.6.2
        Example on CD | Worksheet A,B on CD
        5.6.2
        Example C,D: True Shape of Planar Figure - Revolution of a Plane
        5.6.2
        Example (ppsx) | Worksheet C,D (pdf)
      • 5.6.3
        Example A: Equilateral Triangle - Revolution of a Plane
        5.6.3
        Example on CD | Worksheet A,B on CD
        5.6.3
        Example B: Square - Revolution of a Plane
        5.6.3
        Example on CD
        5.6.3
        Example C: Square - Revolution of a Plane
        5.6.3
        Example (ppsx) | Worksheet C,D (pdf)
        5.6.3
        Example D: Equilateral Triangle - Revolution of a Plane
        5.6.3
        Example (ppsx)
    • 5.7 Solid Intersected by Plane
      • 5.7.0
        Example: Pyramid Intersected by a Plane of Edge View
        5.7.0
        Example on CD | Worksheet on CD
    • 5.8 Intercept of Straight Line with Plane
      • 5.8.1
        Example: Intercept of Straight Line with Plane -"Cover Line"
        5.8.1
        Example on CD | Worksheet on CD
      • 5.8.2
        Example A: Line Intersects a Plane- Edge View Method
        5.8.2
        Example on CD | Worksheet on CD
        5.8.2
        Example B: Line Intersects a Plane- Edge View Method
        5.8.2
        Example on CD
      • 5.8.3
        Example: Intersection of Prism with Plane- Development
        5.8.3
        Example (ppsx) | Worksheet (pdf)
      • 5.8.4
        Example: Intersection of Line with Prism
        5.8.4
        Example (ppsx) | Worksheet (pdf)
      • 5.8.5
        Example: Intersection of Line with Pyramid
        5.8.5
        Example (ppsx) | Worksheet (pdf)
      • 5.8.6
        Example A: Interception Line of Two Triangles
        5.8.6
        Example (ppsx) | Worksheet A-D (pdf)
        5.8.6
        Example B: Interception Line of Two Triangles
        5.8.6
        Example (ppsx)
        5.8.6
        Example C: Interception Line of Two Triangles
        5.8.6
        Example (ppsx)
        5.8.6
        Example D: Interception Line of Two Triangles
        5.8.6
        Example (ppsx)
    • 5.9 Law of Right Angle
      • 5.9.0
        Law of Right Angle
        5.9.0
        Theory on CD
      • 5.9.1
        Example: Perpendicular Line to a Plane
        5.9.1
        Example on CD | Worksheet on CD
      • 5.9.2
        Example A,B: Perpendicular Line to a Triangle
        5.9.2
        Example on CD | Worksheet A,B on CD
        5.9.2
        Example C,D: Perpendicular Line -Squared Pyramid
        5.9.2
        Example (ppsx) | Worksheet C,D (pdf)
      • 5.9.3
        Perpendicular Plane to a Straight Line
        5.9.3
        Theory on CD
      • 5.9.4
        Example: Perpendicular Plane to a Line and its Intercept
        5.9.4
        Example on CD | Worksheet (pdf)
        5.9.4
        Example C,D: Perpendicular Plane - Squared Pyramid
        5.9.4
        Example (ppsx)
    • 5.10 Shortest Distance
      • 5.10.0
        Example: Distance between a Point and a Line - Auxiliary Views
        5.10.0
        Example on CD | Worksheet on CD
      • 5.10.1
        Example: Shortest Distance between a Point and a Plane - Intercept
        5.10.1
        Example on CD | Worksheet on CD
      • 5.10.2
        Example: Distance between Point and Plane - Auxiliary Views
        5.10.2
        Example on CD | Worksheet on CD
    • 5.11 Development
      • 5.11.1
        Example: Development of a Truncated Pyramid
        5.11.1
        Example (ppsx) | Worksheet (pdf)
      • 5.11.2
        Example A: Truncated Pyramid Cut by Prism
        5.11.2
        Example (ppsx) | Worksheet (pdf)
        5.11.2
        Example B: Development of a Truncated Pyramid Cut by Prism
        5.11.2
        Example (ppsx)
  • 6 Shadow
    • 6.1 Terms and Properties
      • 6.1.0
        Shadow of Parallel Projection - Fundamental Terms
        6.1.0
        Theory on CD
      • 6.1.1
        Example 1: Shadow of a Cuboid
        6.1.1
        Example on CD | Worksheet on CD
      • 6.1.2
        Example 2: Shadow of Cuboids
        6.1.2
        Example on CD | Worksheet on CD
      • 6.1.3
        Example 3: Shadow of Cuboids
        6.1.3
        Example on CD | Worksheet on CD
      • 6.1.4
        Example 4: Shadow of Cuboids
        6.1.4
        Example on CD | Worksheet on CD
      • 6.1.5
        Example 5: Shadow of Cuboids
        6.1.5
        Example on CD | Worksheet on CD
      • 6.1.6
        Example 6: Shadow of Cuboid and Ramp
        6.1.6
        Example on CD | Worksheet on CD
    • 6.2 Application: Shadow of Buildings
      • 6.2.1
        Example 1: Shadow of a Building
        6.2.1
        Example on CD | Worksheet on CD
      • 6.2.2
        Example 2: Shadow of a Wall and a Ramp
        6.2.2
        Example on CD | Worksheet on CD
      • 6.2.3
        Example 3: Shadow of a House with Chimney
        6.2.3
        Example on CD | Worksheet on CD
      • 6.2.4
        Example 4: Shadow of a Church
        6.2.4
        Example on CD | Worksheet on CD
      • 6.2.5
        Example 5: Shadow of an Entrance with Canopy
        6.2.5
        Example on CD | Worksheet on CD
      • 6.2.6
        Example 6: Shadow of a Roof with Dormer
        6.2.6
        Example on CD | Worksheet on CD
    • 6.3 Application: Shadow of Churches
      • 6.3.1
        Example 1: Shadow of a Church
        6.3.1
        Example on CD | Worksheet on CD
      • 6.3.2
        Example 2: Shadow of a Church
        6.3.2
        Example on CD | Worksheet on CD
      • 6.3.3
        Example 3: Shadow of a Church
        6.3.3
        Example on CD | Worksheet on CD
      • 6.3.4
        Example 4: Shadow of a Church
        6.3.4
        Example on CD | Worksheet on CD
      • 6.3.5
        Example 5: Shadow of a Church
        6.3.5
        Example on CD | Worksheet on CD
  • 7 Special (Planar) Curves
    • 7.1 Ellipse
      • 7.1.0
        Definition of an Ellipse - Ellipsoid
        7.1.0
        Theory on CD | Worksheet on CD
      • 7.1.1
        Circles of Curvature of an Ellipse
        7.1.1
        Theory on CD | Worksheet on CD
      • 7.1.2
        Construction of an Ellipse with a Wrapper and its Reversion
        7.1.2
        Theory on CD | Worksheet on CD
      • 7.1.3
        Construction of an Ellipse by de la Hire
        7.1.3
        Theory on CD
      • 7.1.4
        Construction of Axes of an Ellipse by Rytz - Conjugate Diameters
        7.1.4
        Theory on CD | Worksheet on CD
    • 7.2 Parabola
      • 7.2.0
        Definition and Construction of a Parabola
        7.2.0
        Theory on CD | Worksheet on CD
    • 7.3 Hyperbola
      • 7.3.0
        Definition and Construction of a Hyperbola
        7.3.0
        Theory on CD | Worksheet on CD
      • 7.3.1
        Constructions of a Hyperbola with Dividers
        7.3.1
        Theory on CD | Worksheet on CD
    • 7.4 Bezier curves
      • 7.4.0
        Construction and Parametric Equations of Bezier Curves
        7.4.0
        Theory on CD | Worksheet A,B on CD | Worksheet C,D (pdf)
  • 8 Normal Projection of a Circle and Sphere
    • 8.1 Circle in the Plan and Front View
      • 8.1.0
        Normal Projection of a Circle
        8.1.0
        Theory on CD
      • 8.1.1
        Example: Image of a Circle in a Plane of Edge View
        8.1.1
        Example on CD | Worksheet on CD
      • 8.1.2
        Example: Circumcircle of a Triangle in a Plane of Edge View
        8.1.2
        Example on CD | Worksheet on CD
      • 8.1.3
        Example: Image of a Circle in an Oblique Plane
        8.1.3
        Example on CD | Worksheet on CD
      • 8.1.4
        Example: Point Rotates about an Axis (= Principle Line)
        8.1.4
        Example on CD | Worksheet on CD
      • 8.1.5
        Example: Point Rotates about an Axis
        8.1.5
        Example on CD | Worksheet on CD
      • 8.1.6
        Example: Example: Rotational Cylinder- Third Edge View Circle
        8.1.6
        Example (ppsx) | Worksheet (pdf)
    • 8.2 Axonometric View of Circle
      • 8.2.1
        Example A: Axonometric Image of a Circle
        8.2.1
        Example on CD | Worksheet on CD
        8.2.1
        Example B: Axonometric Image of a Circle
        8.2.1
        Example on CD
      • 8.2.2
        Example: Isometric View of Circles
        8.2.2
        Example on CD
        8.2.2
        Example: Isometry of Circles
        8.2.2
        Worksheet on CD
    • 8.3 Sphere
      • 8.3.1
        Sphere- Fundamental Terms
        8.3.1
        Theory on CD | Worksheet (pdf)
      • 8.3.2
        Sphere- Properties
        8.3.2
        Theory on CD | Worksheet (pdf)
      • 8.3.3
        Sphere and Geography
        8.3.3
        Theory on CD
      • 8.3.4
        Tangent Plane of a Sphere
        8.3.4
        Theory on CD | Worksheet (pdf)
    • 8.4 Define Points and Tangent Lines
      • 8.4.1
        Example: Locate Point on a Sphere
        8.4.1
        Example on CD | Worksheet on CD
      • 8.4.2
        Example: Locate Point on a Sphere and Define its Tangent Plane
        8.4.2
        Example on CD | Worksheet on CD
    • 8.5 Sphere Cut by Planes
      • 8.5.1
        Example: Intersection of a Sphere with a Plane of Edge View
        8.5.1
        Example on CD | Worksheet on CD
      • 8.5.2
        Example: Intersection of a Sphere with an Oblique Plane
        8.5.2
        Example on CD | Worksheet on CD
      • 8.5.3
        Example A: Sphere Cut by Planes of Edge View
        8.5.3
        Example on CD | Worksheet A on CD
        8.5.3
        Example B: Sphere Cut by Planes of Edge View
        8.5.3
        Example (ppsx) | Worksheet B (pdf)
      • 8.5.4
        Example: Intercepts of Line with Sphere
        8.5.4
        Example on CD | Worksheet on CD
      • 8.5.5
        Example: Dome of Sphere- Third Edge View of Circle
        8.5.5
        Example (ppsx) | Worksheet (pdf)
      • 8.5.6
        Example: Snowman- Third Edge View of Circle
        8.5.6
        Example (ppsx) | Worksheet (pdf)
      • 8.5.7
        Example: Top Hat- Third Edge View of Circle
        8.5.7
        Example (ppsx) | Worksheet (pdf)
    • 8.6 Sphere defined by
      • 8.6.1
        Example: Sphere Given by Midpoint and Tangent Plane
        8.6.1
        Example on CD | Worksheet on CD
      • 8.6.2
        Example: Sphere Defined by Midpoint and Tangent Line
        8.6.2
        Example on CD | Worksheet on CD
      • 8.6.3
        Example: Sphere Defined by Three Points on a Great Circle
        8.6.3
        Example on CD | Worksheet on CD
      • 8.6.4
        Example: Sphere Defined by 3 Points on a Small Circle and Radius
        8.6.4
        Example on CD | Worksheet on CD
      • 8.6.5
        Example: Sphere Defined by Point and its Tangent Plane
        8.6.5
        Example on CD | Worksheet on CD
  • 9 Intersection of a Cylinder
    • 9.1 Cylinder Cut by Plane
      • 9.1.0
        Intersection of a Cylinder with a Plane
        9.1.0
        Theory on CD
      • 9.1.1
        Example A: Cylinder Cut by Plane - Points, Tangent Lines
        9.1.1
        Example on CD | Worksheet on CD
        9.1.1
        Example B: Cylinder Cut by Plane - Axes Direct
        9.1.1
        Example on CD
        9.1.1
        Example C: Cylinder Cut by Plane - Rytz
        9.1.1
        Example on CD
      • 9.1.2
        Example: Intersection of Line with Cylinder
        9.1.2
        Example (ppsx) | Worksheet (pdf)
      • 9.1.3
        Example: Intersection of Cylinder with Plane- Development
        9.1.3
        Example (ppsx) | Worksheet (pdf)
    • 9.2 Application: Cylinder Cut by Prism - Axonometry
      • 9.2.1
        Example: Intersection of a Circular Cylinder with a Prism
        9.2.1
        Example on CD | Worksheet on CD
      • 9.2.2
        Example: Entrance of Hall 1
        9.2.2
        Example on CD | Worksheet on CD
      • 9.2.3
        Example: Intersection of a Chimney with Roof Faces
        9.2.3
        Example on CD | Worksheet on CD
      • 9.2.4
        Example: Entrance of Hall 2
        9.2.4
        Example on CD | Worksheet on CD
    • 9.3 Intersection of Two Circular Cylinders - Axonometry
      • 9.3.0
        Intersection Curves of Two Cylinders
        9.3.0
        Theory on CD
      • 9.3.1
        Example A: Cylinders with the Same Tangential Plane
        9.3.1
        Example on CD | Worksheet on CD
        9.3.1
        Example B: Cylinder Cut by Part of a Second Cylinder
        9.3.1
        Example on CD
      • 9.3.2
        Example A: Cylinder Drilled by Smaller Cylinder
        9.3.2
        Example on CD | Worksheet (pdf)
        9.3.2
        Example B: Cylinder Cut by Cylinder- Locomotive
        9.3.2
        Example (ppsx)
      • 9.3.3
        Example A: Cross Vault
        9.3.3
        Example on CD | Worksheet on CD
        9.3.3
        Example B: Ellipses as Intersection Curves of Two Cylinders
        9.3.3
        Example on CD
      • 9.3.4
        Example: Pipe Connection - Auxiliary Sphere
        9.3.4
        Example (ppsx) | Worksheet (pdf)
    • 9.4 Principle Views : Cylinder Cut by Prism
      • 9.4.1
        Example: Intersection of a Circular Cylinder with a Prism
        9.4.1
        Example on CD | Worksheet on CD
  • 10 Intersection Curves of Circular Cone with a Plane
    • 10.1 Intersection Curves of a Circular Cone
      • 10.1.0
        Circular Cone Intersected by Plane
        10.1.0
        Theory on CD | Worksheet (pdf)
      • 10.1.1
        Example: Basic Constructions of a Cone - Locate Point
        10.1.1
        Example on CD | Worksheet on CD
      • 10.1.2
        Construction of Outline Points of Rotational Cone
        10.1.2
        Theory (ppsx) | Worksheet (pdf)
      • 10.1.3
        Example A,B: Rotational Cone- Basement Shows Edge View
        10.1.3
        Example (ppsx) | Worksheet A,B (pdf)
      • 10.1.4
        Example: Cup- Truncated Cone with Circles of Third Edge View
        10.1.4
        Example (ppsx) | Worksheet (pdf)
      • 10.1.5
        Example: Ice Cream- Circles Shows Second Edge View
        10.1.5
        Example (ppsx) | Worksheet (pdf)
    • 10.2 Ellipse as a Curve on a Circular Cone
      • 10.2.1
        Example A: Cone Intersected by Planes - Ellipses
        10.2.1
        Example on CD | Worksheet on CD
        10.2.1
        Example B: Cone Intersected by Planes - Ellipses
        10.2.1
        Example on CD
    • 10.3 Hyperbola as a Curve on a Circular Cone
      • 10.3.1
        Example: Cone Intersected by a Plane - Hyperbola
        10.3.1
        Example on CD
        10.3.1
        Example: Cone Intersected by a Plane - Hyperbola
        10.3.1
        Worksheet on CD
    • 10.4 Parabola as a Curve on a Circular Cone
      • 10.4.1
        Example A: Cone Intersected by Planes - Parabolas
        10.4.1
        Example on CD | Worksheet on CD
        10.4.1
        Example B: Cone Intersected by Planes - Parabolas
        10.4.1
        Example on CD
  • 11 Helix and Helical Surfaces
    • 11.1 Helical Motion
      • 11.1.0
        Helical Motion and Helix
        11.1.0
        Theory on CD | Worksheet (pdf)
      • 11.1.1
        Special Helical Surfaces
        11.1.1
        Theory (ppsx)| Worksheet (pdf)
      • 11.1.2
        Developable Helical Surfaces- Evolvent- Evolute
        11.1.2
        Theory (ppsx)
    • 11.2 Helix and Helical Surfaces in Principle Views
      • 11.2.1
        Example A: Right-handed Helix
        11.2.1
        Example on CD | Worksheet (pdf)
        11.2.1
        Example B: Right-handed Helical Surface
        11.2.1
        Example (ppsx)
      • 11.2.2
        Example: Left-handed Helical Surface of a Square
        11.2.2
        Example on CD | Worksheet on CD
      • 11.2.3
        Example: Helical Surfaces of Helical Tangent Line
        11.2.3
        Example (ppsx) | Worksheet (pdf)
    • 11.3 Helix and Helical Surface in Axonometric View
      • 11.3.1
        Example: Axonometric View of a Right-handed Helical Surface
        11.3.1
        Example on CD | Worksheet on CD
    • 11.4 Application of Helical Surfaces
      • 11.4.1
        Example: Object Analysis- Candle Stick
        11.4.1
        Example (ppsx) | Worksheet (pdf)
      • 11.4.2
        Example: Object Analysis- Bicycle Rack 1
        11.4.2
        Example (ppsx) | Worksheet (pdf)
      • 11.4.3
        Example: Object Analysis- Bicycle Rack 2
        11.4.3
        Example (ppsx) | Worksheet (pdf)
      • 11.4.4
        Example: Object Analysis- Vase
        11.4.4
        Example (ppsx) | Worksheet (pdf)
  • 12 Central Projection
    • 12.1 Fundamental Terms
      • 12.1.0
        Fundamental Terms of Central Projection
        12.1.0
        Theory on CD | Worksheet (pdf)
    • 12.2 Bisection and Duplication
      • 12.2.0
        Bisection and Duplication of Segments
        12.2.0
        Theory on CD
      • 12.2.1
        Example 1: Bisection- Part of a Cube
        12.2.1
        Example on CD | Worksheet on CD
      • 12.2.2
        Example 2: Bisection- Part of a Cube
        12.2.2
        Example on CD | Worksheet on CD
      • 12.2.3
        Example 3: Duplication- Part of a Cube
        12.2.3
        Example on CD | Worksheet on CD
      • 12.2.4
        Example 4: Duplication- Part of a Cube
        12.2.4
        Example on CD | Worksheet on CD
      • 12.2.5
        Example: Reflection of a Solid about a Plane
        12.2.5
        Example on CD | Worksheet on CD
      • 12.2.6
        Example: Rotation (90°) of a Solid about an Axis
        12.2.6
        Example on CD | Worksheet on CD
      • 12.2.7
        Example 2: Bisection- Part of a Cube
        12.2.7
        Example (ppsx) | Worksheet (pdf)
      • 12.2.8
        Example: Octahedron by Bisection
        12.2.8
        Example (ppsx) | Worksheet (pdf)
      • 12.2.9
        Example: Duplication- Regular Hexagonal Prism
        12.2.9
        Example (ppsx) | Worksheet (pdf)
      • 12.2.10
        Example: Duplication and Bisection- Church
        12.2.10
        Example (ppsx) | Worksheet (pdf)
    • 12.3 Perspective View by Plan and Front View
      • 12.3.0
        Perspective View - Using Plan and Front View
        12.3.0
        Theory on CD
      • 12.3.1
        Example: Cuboid
        12.3.1
        Example on CD | Worksheet on CD
      • 12.3.2
        Example: House
        12.3.2
        Example on CD | Worksheet on CD
      • 12.3.3
        Example: Tent
        12.3.3
        Example on CD | Worksheet on CD
      • 12.3.4
        Example: Obelisk
        12.3.4
        Example on CD | Worksheet on CD
      • 12.3.5
        Example: House with Bay
        12.3.5
        Example on CD | Worksheet on CD
      • 12.3.6
        Example: Corner House
        12.3.6
        Example on CD | Worksheet on CD
    • 12.4 Perspective View by Plan View and Intercept with Image Plane
      • 12.4.0
        Perspective View: Plan View and Intercept with Image Plane
        12.4.0
        Theory on CD
      • 12.4.1
        Example: Cuboid
        12.4.1
        Example on CD | Worksheet on CD
      • 12.4.2
        Example: House with a Tent Roof
        12.4.2
        Example on CD | Worksheet on CD
      • 12.4.3
        Example: House with Saddleback Roof 1
        12.4.3
        Example on CD | Worksheet on CD
      • 12.4.4
        Example: House with Saddleback Roof 2
        12.4.4
        Example on CD | Worksheet on CD
      • 12.4.5
        Example: House with Dormer
        12.4.5
        Example on CD | Worksheet on CD
      • 12.4.6
        Example: Corner House
        12.4.6
        Example on CD | Worksheet on CD
      • 12.4.7
        Example: House with Bay
        12.4.7
        Example on CD | Worksheet on CD
      • 12.4.8
        Example: Bus Stop
        12.4.8
        Example on CD | Worksheet on CD
      • 12.4.9
        Example: Church
        12.4.9
        Example on CD | Worksheet on CD
      • 12.4.10
        Example: Church 2
        12.4.10
        Example (ppsx) | Worksheet (pdf)
    • 12.5 Advanced Constructions
      • 12.5.0
        Perspective View: Transferring Segments
        12.5.0
        Theory on CD
      • 12.5.1
        Rotation of the Basement into the Image Plane
        12.5.1
        Theory on CD

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