chaptersolidsandtheirintersections.ppt

Company name LOGO Chapter 03 Solids and Their IntersectionsⅢ Presented by YANG Zhi-Liing Contents 1.Intersection of Planes and a Curved Solid 2. Intersection of Planes and a Composite Solid Exercise 1: Complete the left-side view. 1‘(2’) 2 1 2’’ 1’’ 3(4) 1(2) 1’(3’) 2’(4’) 3’’ 1’’ 4’’ 2’’ 5’(6’) 7’(8’) 6(8) 5(7) 5’’ 6’’ 7’’ 8’’ Exercise 2: Complete the left-side view. Exercise 3: Complete the left-side view. 1’(2’) 1’’ 2’’ 3’(4’) 5’(6’) 4 3 6 5 6’’ 5’’ 4’’ 3’’ Intersection of Planes and a Cone When the right cone is cut by a plane, there will be five situations depending on the relative position of the cutting plane and the axis of the cone. Intersection of a Plane and a Cone Pass through the vertex of the cone Two straight lines PV A circle PV θ θ= 90° Intersection of a Plane and a Cone A parabola PV θ α θ=α A hyperbola PV α θ= 0°＜α PV A ellipse α θ θ＞α Exercise 4: Complete the top view and add a left side view. How to find another axis? Exercise 4: Complete the top view and add a left side view. Example 2: Complete the frontal view and the top view. Example 2: Complete the frontal view and the top view. 1”(2”) 3”(4”) 5”(6”) 7” Example 2: Complete the frontal view and the top view. 1 2 1’ 2’ Example 2: Complete the frontal view and the top view. 3’ 4’ 3 4 5 6 5’ 6’ 7’ 7 Example 2: Complete the frontal view and the top view. Intersection of Planes and a Sphere If a sphere is cut by a plane, the intersection is a circle or an arc. But the circle with different position will produce different projection. Example 3: Complete the given views of the sphere cut by three planes. Example 3: Complete the given views of the sphere cut by three planes. Intersection of Planes and a Composite Solid A composite solid is composed of some basic geometric solids. When some curved surfaces of a composite solid is cut by a plane, the intersection should be drawn one by one. ● ● ● ● Example 4: Draw the left side view. Example 4: Draw the left side view. Exercise 4: Draw the lef