Some key Geometric Principles t4（一些关键几何原则t4）.pdfVIP

Some key Geometric Principles 1. A line projects as a true length when a view is taken looking perpendicular to the line  A line parallel to the VP will appear as a true length in elevation  A line parallel to the HP will appear as a true length in plan 2. Parallel lines appear parallel in every orthographic view 3. If a line is parallel to any line on a plane, it is parallel to the plane 4. A line projects as a point when we look along its true length 5. A plane projects as an edge when any line on the plane projects as a point 6. The true shape of a plane is seen on a projection plane which is parallel to the plane 7. Two planes intersect in a line 8. The dihedral angle between two planes is seen in a view showing the planes as edges 9. The true angle between a line and a plane is seen in a view showing the line as a true length and the plane as an edge 10. All horizontal sections of an upright or inverted right cone are circles 11. A sphere appears as a circle in every view 12. A sphere and cone in contact will have a common tangent plane 13. When two spheres touch one another:  the point of contact lies on the line joining the two centres  the distance between their centres is equal to the sum of the radii  the point of contact can be located in any view, by dividing the line in the ratio of the radii 14. The vertical trace of a plane is the line in which the plane meets the V.P. 15. The horizontal trace of a plane is the line in which the plane meets the H.P. A line projects as a true length when a view is taken looking perpendicular to the line Parallel lines appear parallel in every orthographic view If a line is parallel to any line on a plane, it is parallel to the plane A line projects as a point when we look along its true length A plane projects as an edge when any line on the plane projects as a