2. Introduction
This document shows how to determine whether two bounded cylinders intersect. The
algorithm uses
the method of separating axes, although the construction is more complicated than one
encounters when
separating convex polyhedra. The resulting algorithm is a fairly expensive one. If you
plan on using cylinders
for bounding volumes in a real-time graphics engine—think twice. A better alternative to
a cylinder is a
capsule, the set of points a specified distance from a line segment. Two capsules intersect
if and only if the
distance between capsule line segments is smaller or equal to the sum of the capsule radii,
a much cheaper
test to perform.
3. Intersection of cylinder and cylinder
Intersection of Cylinder and Cylinder
The line of intersection between cylinders will be curved since the lateral surfaces of
cylinders are curved. Points on the intersection line can be located by either line
method or cutting plane method. For plotting an accurate curve, the points at which
the curve changes direction must also be located. These points lie on the outermost or
extreme lines of each cylinder pierce the surface of the other cylinder. For obtaining
the intersection of cylinder and cylinder, cutting plane method is more useful. In this
technique, a series of horizontal cutting planes are assumed to be passing through the
lines of the horizontal cylinder and these planes cuts both cylinders as shown in figure
3. After each sectioning, the top view of the section of the horizontal cylinder will be
a rectangle with its width depending on the position of the cutting plane, where as the
top view of the vertical cylinder will be a circle with diameter equal the diameter of
the vertical cylinder. The points at which the sides of the rectangles intersect the
circle will lie on the curve of intersection
4. Problem :
A vertical cylinder of 80 mm
diameter is completely penetrated
by another cylinder of 60 mm
diameter, their axes bisecting each
other at right angles. Draw their
projections showing curves of
penetration, assuming the axis of
the penetrating cylinder to be
parallel to the VP.
5. Method to draw Cylinder to cylinder intersection
First draw the Top View make 50mm diameter
circle and project all axis line for the side view
and front view
Make 70mm axis height of front view and side
view
From center of rectangular side view make
40mm circle this is the intersect cylinder and
make its projection for top view and draw the
intersect cylinder in top view with 70mm
horizontal line and 40mm diameter of circle.
Project the line for intersect cylinder in front
view help of top view
Using all intersect point match all projection
with the help of naming
This id the Cylinder to cylinder intersection
7. Type of cylinder to cylinder intersection
Examples of the intersection of two cylinders
a one-branch curve, which occurs when one cylinder passes only partially
through the other.
( This type of intersection is called partial intersection .)
a two-branch curve, which occurs when one cylinder passes completely
through the other.
( This type of intersection is called complete intersection.)
a curve of the 4th order with one double points, which occurs when the
cylinders have a common tangent plane.
9. Application of cylinder to cylinder
intersection
We will used cylinder to cylinder
intersection in engine valves design .
Also we used in manufacture of
plumbing tools
It is also used in manufacture of
different type of boiler to perform large
amount of work by intersecting two
cylindrical pipe
We used cylinder to cylinder
intersection to make underground water
supply for one place to other place
11. A machine component having
two intersecting cylindrical
surfaces with the axis at
acute angle to each other.
An Industrial Dust collector.
Intersection of two cylinders. Intersection of a Cylindrical
main and Branch Pipe.
Two Cylindrical
surfaces.
SOME ACTUAL OBJECTS ARE SHOWN, SHOWING CURVES OF
INTERSECTIONS.
