Example Intersection of Line with Cylinder Additional Task

Example: Intersection of Line with Cylinder Additional Task to the multimedia book „Darstellende Geometrie/ 3 D-Geometry“, published by Veritas Educational Edition Student Edition ISBN - 978 -3 -7058 -9079 -4 ISBN - 978 -3 -7058 -9293 -4 Special edition for teachers: The print version shows handouts of theory and worked-out examples. Each handout can be printed in colour and is also suitable as a solutions handout. Through the use of animated Power. Point files it is possible to structure the lessons in a contemporary and innovative manner for students. Special edition for students: The print version consists of well prepared worksheets to start working right away. On the CD you will find colourful Power. Point presentations, including theory as well as solved examples with step-by-step explanations. This provides a highly efficient technique in developing an understanding of geometry and its concepts. for more DETAILS and ORDER 1

Example: Intersection of Line with Cylinder a) A cylinder is intersected by line g [PQ]. Determine the plan and front view of the intersection. Use an auxiliary plane, which is parallel to the generatrices of the cylinder. This plane is a plane of first edge view. Q‘‘ Define the intersection of that plane with the cylinder. Q g‘‘ p 1‘‘ = p 2‘ P‘‘ g Q‘ P P‘ g‘ e 1‘ e 2‘ g‘ Q‘ 2

Example: Intersection of Line with Cylinder a) A cylinder is intersected by line g [PQ]. Determine the plan and front view of the intersection. The intersection lines are generatrices of the cylinder. The required points are the intercepts of these generatrices with line g. Q‘‘ g‘‘ Show proper visibility. e 2‘‘ e 1‘‘ Q e 1 p 1‘‘ = p 2‘ P‘‘ g e 2 Q‘ P P‘ g‘ e 1‘ e 2‘ g‘ Q‘ 3

Example: Intersection of Line with Cylinder b) A cylinder is intersected by line g [PQ]. Determine the plan and front view of the intersection. P‘‘ g‘‘ Choose an auxiliary plane through the line g, which intersects the cylinder along simple lines. An auxiliary plane parallel to the generatrices of the cylinder intersects the cylinder along generatrices. Q‘‘ p 1‘‘ = p 2‘ Define the intersection line of the auxiliary plane with the basement of the cylinder. Q‘ Determine the intercepts of the intersection line with the base circle of the cylinder. Construct the according generatrices of the cylinder through these intercepts and define the intercepts of these generatrices with line g. P‘ g‘ 4

Example: Intersection of Line with Cylinder b) A cylinder is intersected by line g [PQ]. Determine the plan and front view of the intersection. P‘‘ g‘‘ Show proper visibility of line g with respect to the cylinder. Consider the visibility in the plan view: The part of line g, between point P and intercept, is visible. Q‘‘ p 1‘‘ = p 2‘ Q‘ The further part lies either within the cylinder or is behind the cylinder. P‘ g‘ 5

Example: Intersection of a Line with a Cylinder b) A cylinder is intersected by line g [PQ]. Determine the plan and front view of the intersection. P‘‘ g‘‘ Show proper visibility of line g with respect to the cylinder. Consider the visibility in the front view: Construct the images of the outline generatrices (of the front view) in the plan view. Q‘‘ p 1‘‘ = p 2‘ Q‘ Define the responsible line of sight s 2. Both intercept lie beyond that plane. Therefore line g is hidden by the cylinder. P‘ g‘ s 2 6

Example: Intersection of Line with Cylinder b) A cylinder is intersected by line g [PQ]. Determine the plan and front view of the intersection. P‘‘ g‘‘ Show proper visibility of line g with respect to the cylinder. Q‘‘ p 1‘‘ = p 2‘ Q‘ P‘ g‘ s 2 7