Diedric system. Elements. Point, straight line and plane. Figure
see the two planes that intersect orthogonally, and on which objects are projected, the plant (horizontal) and the elevation (vertical). The two planes divide the space into four parts: the first, second, third and fourth quadrant.
can use a different projection plane to provide more information about the object being represented. This map is called profiling and is perpendicular to the ground line, which is the intersection of the floor plan and elevation (in magenta).
observe the division into four quadrants (from 1 to 4 °) generated floor plans and elevation.
The three projection planes divide the space into 8 pieces.
The representation of a dihedral point system is given by its orthogonal projections on three planes: a point P is transformed into its 3 projections P1 P2 P3.
Then the plans are open until they are all coplanar, turn the plane profile 90 ° to the vertical and once left in the same plane as it , turn the vertical (and in profile, who are already the same plane) 90 ° to the horizontal, so we have 3 planes coincide with the paper in that we represent. The turn of the plans shows that the projections of the point will always are aligned perpendicular to the line of intersection of each pair of planes. All that part of space: the point P, its projection lines (from P to P1, P2 P, etc.) Disappears. In dihedral only represents what is projected on the 3 planes of projection.
dihedral So are the views of one point: the plan, elevation and profile are always correlated.
Plans Plans
projection
A plane is represented by the intersection with the planes of projection, these intersections are called traces. The red plane intersects the planes of projection according to the plans a1 (horizontal trace) a2 (vertical trace) a3 (profile trace).
Theorem for all levels: the trace of a plane always intersect at one point on the ground line. (For a straight-LT-cut to a plane at one point, if you do it in two or more is that is contained therein, in this case all traces agree points on the LT, it is said that the plane passes through the LT).
An oblique plane trace c has its oblique (not orthogonal) with respect to the ground line.
Other oblique plane.
Plans
the first bisector bisectors second 1b and 2b, bisect the horizontal plane and vertical.
map projecting ridge or vertical trace is vertical and horizontal oblique a2 a1 orthogonal to the LT.
f Frontal plane: parallel to the vertical and horizontal trace is parallel to the LT.
h horizontal plane parallel to the horizontal and vertical trace h2es parallel to the LT.
plane parallel to the LT: p1 p2 has its traces parallel to the LT.
plane through the ground line, has its traces in the LT.
vertical plane, the vertical trace a2 is vertical, the horizontal should be oblique, but we have a flat profile.
Straight Lines are represented by their projections but can also be defined by its trace (points where it cuts the planes of projection).
The line to and their projections that define: a1 a2.
Their trace has vertical and horizontal Va.
A line is defined by two projections may be your plan and elevation or plan and profile or standard profile, etc.
The penetrates straight going over the 2 nd quadrant below have in the 4 th quadrant and its projections are visible in the 1 st quadrant. By convention the parties do not represent discontinuous visible.
Here we have the same straight dihedral system defined in its projections a1 a2 with the quadrants through which it passes.
Here we see the representation of an oblique line with its traces on the horizontal and vertical Hr Vr.
dihedral representation of the previous line
A front straight, parallel to vertical and oblique to the horizontal.
A line parallel to the LT.
A profile, which may be included in a plane orthogonal to the LT. The particular case of the profile are the horizontal, vertical and passing through the LT.
A straight-edge, orthogonal to the PV.
A vertical, orthogonal to PH.
planes Lines and dihedral system
The lines are represented by their projections and are shown in red all the traces which are the points where they cut to the planes of projection.
1 - Vertical
2 - De punta
3 - Oblique
4 - Oblique
5 - Horizontal
6 - Front
7 - What happens on the ground line
8 - In profile
9 - In profile, which passes through ground line and is included in the first bisector.
planes are represented by their traces are the lines where they cut to the planes of projection.
10 - Vertical or horizontal projecting
11 - 12
Oblique - Oblique
13 - Horizontal
14 - Front
15 - De ridge or vertical projecting
16 - In profile
17 - What happens on the ground line
18 - Parallel to ground line.
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