Single-curved surfaces are generated by moving a straight line along a curved path such that any two consecutive positions of the generatrix are either parallel (cylinder), intersecting (cone), or tangent to a double-curved line (convolute). A cone is a single-curved-surface primitive formed by a line (generatrix) moving along a curved path such that the line always passes through a fixed point, called the vertex. Each position of the generatrix is called an element of the surface. There are three basic classifications of cones: ■ If the axis is perpendicular to the base, the axis is called the altitude and the cone is called a right con e. ■ If the axis is not perpendicular to the base, the cone is called an oblique cone . ■ If the cone is cut off, it is called a truncated cone or a frustum of a cone. There are many applications for cones in engineering design, including: the nose cone of rockets; transition pieces for heating, ventilating, and air-conditioning systems; conical roof sections; and construction cones used to alert people to construction areas. Cones are represented in multiview drawings by drawing the base curve, vertex, axis, and limiting elements in each view. Conic sections are 2-D plane figures produced by passing an imaginary plane at various angles through a solid (3-D) right circular cone. A cylinder is a single-curved ruled surface formed by a vertical, finite, straight-line element (generatrix) revolved parallel to a vertical or oblique axis directrix and tangent to a horizontal circular or elliptical directrix. The line that connects the center of the base and the top of a cylinder is called the axis. If the axis is perpendicular to the base, the cylinder is a right cylinder . If the axis is not perpendicular to the base, the cylinder is an oblique cylinder . A multiview drawing of a right circular cylinder shows the base curve (a circle), the extreme elements, and the axis. A convolute is a single-curved surface generated by a straight line moving such that it is always tangent to a double-curved line. A tangent plane generation convolute is formed by the path taken by a plane tangent to two curved lines. A polyhedron is a symmetrical or asymmetrical 3-D geometric surface or solid object with multiple polygonal sides. The sides are plane ruled surfaces, and are called faces, and the lines of intersection of the faces are called the edges. Regular polyhedra have regular polygons for faces. There are five regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. As solids, these are known as the five platonic solids. Regular polyhedra are classified by the shape and number of faces, as follows: Tetrahedron . A symmetrical or asymmetrical 3-D surface or solid object with four equilateral triangular sides. Hexahedron . A symmetrical or asymmetrical 3-D surface or solid object with six quadrilateral sides.
Octahedron . A symmetrical or asymmetrical surface or solid object with eight equilateral triangular sides.
- Fall '09
- Cartesian Coordinate System, Euclidean geometry