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Piercing Point by Cutting-Plane Method:

Piercing Point by Cutting-Plane Method:. AB in the top view is not just a line but the edge view of cutting plane AB. AB intersects plane 123 along line pq. Transfer line of intersection pq to front view: Point p is the intersection with line 13. Point q is the intersection with line 23.

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Piercing Point by Cutting-Plane Method:

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  1. Piercing Point by Cutting-Plane Method: • AB in the top view is not just a line but the edge view of cutting plane AB. • AB intersects plane 123 along line pq. • Transfer line of intersection pq to front view: • Point p is the intersection with line 13. • Point q is the intersection with line 23. • Connect the transferred points p and q. • The intersection of line pq with line AB in the front view is the piercing point. Since line AB is contained in “cutting plane” AB, the intersection of line AB with plane 123 (i.e., the piercing point) is contained in the intersection of “plane” AB with plane 123 (line pq). • The piercing point can be projected to the top view, or a repetition of steps 1-4 can be done, with AB in front view being the cutting plane. • Show correct visibility of lines.

  2. Intersection of Two Planes • Can be located by finding an edge view of one of the planes (needs an auxiliary view). • Can also be located by finding two piercing points. The line of intersection is the line connecting the two piercing points: • Piercing points can be found by Cutting-Plane method • Need to try possible combinations of line vs. plane • No need to construct an auxiliary view • Show correct visibility

  3. True Size of Planes • line of sight is perpendicular to the edge view of the plane • reference plane is parallel to the edge view of the plane • shows true length of the edges of the plane • shows true angle between edges Steps: • Find the edge of the plane (Find point view of any line in the plane.) • Take a reference plane parallel to the edge view.

  4. Angle Between Lines: • needs a view showing the true length of both lines • a view showing the true size of the plane defined by the two lines. Steps: • Create a plane by connecting the endpoint of the lines. • Find the edge view of the plane. • Find the true size of the plane. The view showing the TS is also showing the angle between the lines.

  5. Example: Angle between two lines (by TS of plane) Given the front and top views of lines PQ and PR, find the angle QPR.

  6. Shortest Distance – Point to a Line A. Line Method • Find the point view of the line. • The shortest distance from the point to the line is true length in the view showing the point view of the line. B. Plane Method • Find the TS of the plane containing the line and the point. • The shortest distance from the point to the line is perpendicular to the TL of the line.

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