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To get a true view (length in the projection is equal to length in 3D space) of one of the lines: SU in this example, projection 3 is drawn with hinge line H 2,3 parallel to S 2 U 2. To get an end view of SU, projection 4 is drawn with hinge line H 3,4 perpendicular to S 3 U 3. The perpendicular distance d gives the shortest distance between PR ...
In geometry a conoid (from Greek κωνος 'cone' and -ειδης 'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions: (1) All rulings are parallel to a plane, the directrix plane. (2) All rulings intersect a fixed line, the axis. The conoid is a right conoid if its axis is perpendicular to its directrix ...
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...
In the same way one picks the point on the y axis corresponding to the number y. The line parallel to the y axis going through the first point and the line parallel to the x axis going through the second point will intersect at precisely one point, which will be called the point with coordinates (x, y).
This is the vanishing point corresponding to all parallel lines with slope − b / a in the plane π. All vanishing points associated with different lines with different slopes belonging to plane π will lie on the x′ axis, which in this case is the horizon line. 2.
The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone; for a right cone, this means the cutting plane is perpendicular to the axis. If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a parabola.
Conversely, if one line is perpendicular to a second line, it is also perpendicular to any line parallel to that second line. In the figure at the right, all of the orange-shaded angles are congruent to each other and all of the green-shaded angles are congruent to each other, because vertical angles are congruent and alternate interior angles ...
In any affine space (including a Euclidean space) the set of lines parallel to a given line (sharing the same direction) is also called a pencil, and the vertex of each pencil of parallel lines is a distinct point at infinity; including these points results in a projective space in which every pair of lines has an intersection.
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