General Program Information

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Southwest Isometric View
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Input Definitions

Inputs Needed to Call the Elbow Function

o - the origin, a 3*1 matrix with x,y,z positions corresponding to the point where the elbow will be drawn
Pipe_inr - the inner radius of the elbowThe origin, the center of the radius of curvature of the elbow.
ND - The nominal diameter of the pipe. This value along with the pipe schedule is used to determine other actual dimensions of the elbow
EN - The enumerated pipe schedule type. Each schedule of pipe is represented by a specific number within our code.

Inputs Defined within the Elbow Function

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• x : o₀
• y : o₁
• z : o₂

p2 =

• x : o₀ - ElbowRadius(2*pipe_inr) + ConRaduis(2*pipe_inr)ND) - outerraduis(ND) - zc
• y : o₁ - ElbowRadius(2*pipe_inr) + ConRaduis(2*pipe_inr)ND) - outerraduis(ND) - zc
• z : o₂ - outerradius(2*pipe_inr) + SocketDepth(2*pipe~inr~)outerraduis(ND) - zc

p3 =

• x : o₀
• y : o₁ + ElbowRadius(2*pipe_inrND) + ConRaduis(2*pipe_inr)outerraduis(ND) + zc
• z : o₂ + outerradius(2*pipe_inr) + SocketDepth(2*pipe_inr)outerraduis(ND) + zc

p4 =

• x : o₀ + ElbowRadius(2*pipe_inrND) + outerraduis(2*pipe_inrND)
• y : o₁
• z : o₂

p5 =

• x : o₀ - ElbowRadius(2*pipe_inrND) - pipe_inr)innerD(ND,EN)/2
• y : o₁
• z : o₂

p6 =

• x : o₀
• y : o₁ - ElbowRadius(2*pipe_inrND) - outerraduis(2*pipe_inrND) - zc
• z : o₂ - ConRadius(2*pipe_inrND)

p7 =

• x : o₀ + ElbowRadius(2*pipe_inrND) + outerraduis(2*pipe_inrND) + zc
• y : o₁
• z : o₂ + ConRadius(2*pipe_inrND)

p9 =

• x : o₀
• y : o₁ + ElbowRadius(2*pipe_inrND)
• z : o₂

p10 =

• x : o₀ - SocketDepth(2*pipe~inr~ND)
• y : o₁ + ElbowRadius(2*pipe_inrND)
• z : o₂

p11 =

• x : o₀
• y : o₁ + ElbowRadius(2*pipe_inrND) - ConRaduis(2*pipe_inrND)
• z : o₂

p12 =

• x : o₀ - SocketDepth(2*pipe~inr~ND) - zc
• y : o₁ + ElbowRadius(2*pipe_inrND) - outerraduis(2*pipe_inrND)
• z : o₂

p13 =

• x : o₀ + zc
• y : o₁ + ElbowRadius(2*pipe_inrND) + outerraduis(2*pipe_inrND)
• z : o₂

p14 =

• x : o₀ - SocketDepth(2*pipe~inr~ND)
• y : o₁ + ElbowRadius(2*pipe_inrND) - ConRaduis(2*pipe_inrND)
• z : o₂

p15 =

• x : o₀
• y : o₁

p16 =

...

p17 =

• x : o₀ + ElbowRadius(2*pipe_inrND)
• y : o₁ - SocketDepth(2*pipe~inr~ND)
• z : o₂

p18 =

• x : o₀ - SocketDepth(2*pipe~inr~ND)
• y : o₁ + ElbowRadius(2*pipe_inrND)
• z : o₂

R1 = ElbowRadius(ND) : Radius of curvature of the elbow

R2 = outerraduis(ND) : Outer radius of the elbow

R3 = innerD(ND,EN)/2 : Inner radius of the elbow

R4 = H1 =ConRaduis(ND) : Outer radius of the socket

win1 =

• x : o₀ - ElbowRadius(2*pipe_inrND) - ConRaduis(2*pipe_inr) + ND) - zc
• y : o₁ - ElbowRadius(2*pipe_inrND) - ConRaduis(2*pipe_inr) + ND) - zc
• z : o₂

win2 =

• x : o₀ + ElbowRadius(2*pipe_inrND) + ConRaduis(2*pipe_inrND) + zc
• y : o₁ + ElbowRadius(2*pipe_inrND) + ConRaduis(2*pipe_inrND) + zc
• z : o₂

Note: zc corresponds to the zoom constant used within AutoCAD and can be found in , defined by the basics file that is referenced by the elbow program.

Technical Program Outline

Note: All coordinates are referenced in top view in the program unless otherwise specifiedImage Removed

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zoom_win- zooms on a window space directly around where the elbow is to be drawn

zoom_win <-- zoom_wina(win1,win2)

win1 =

• x : o₀ - ElbowRadius(2*pipe_inrND) - ConRaduis(2*pipe_inr) + ND) - zc
• y : o₁ - ElbowRadius(2*pipe_inrND) - ConRaduis(2*pipe_inr) + ND) - zc
• z : o₂

win2 =

• x : o₀ + ElbowRadius(2*pipe_inrND) + ConRaduis(2*pipe_inrND) + zc
• y : o₁ + ElbowRadius(2*pipe_inrND) + ConRaduis(2*pipe_inrND) + zc
• z : o₂
  

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Top View
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torus_big *torus_big* - Draws the larger torus, a 3 dimensional ring that creates the outer surface of the elbow

torus_big <-- torus(p1,R1,R2)

p1 =

• x : o₀
• y : o₁
• z : o₂

R1 =

R2 =

...

origin

R1 = Radius of curvature of the elbow

R2 = Outer radius of the elbow

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box1 - draws a box slightly larger than the torus, in all dimensions

box1 <-- box(p2,p3)

p2 =

• x : o₀ - ElbowRadius(2*pipe_inr) + ConRaduis(2*pipe_inr)ND) - outerraduis(ND) - zc
• y : o₁ - ElbowRadius(2*pipe_inr) + ConRaduis(2*pipe_inr)ND) - outerraduis(ND) - zc
• z : o₂ - outerradius(2*pipe_inr) + SocketDepth(2*pipe~inr~)outerraduis(ND) - zc

p3 =

• x : o₀
• y : o₁ + ElbowRadius(2*pipe_inrND) + ConRaduis(2*pipe_inrND)
• z : o₂ + outerradius(2*pipe_inrND) + SocketDepth(2*pipe_inr)

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• ND)
  
  

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*After Subtract*
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subtract1 - subtracts the left half of the large torus by using p4 to select the torus as the object to be subtracted from, and using the origin to select the box as the object to be subtracted.subtract1 - removes the box that was drawn over half of the torus in order to make it a half torus
subtract1<-- subtractD(p4,p1)

p4 =

• x : o₀ + ElbowRadius(2*pipe_inrND) + outerraduis(2*pipe_inrND)
• y : o₁
• z : o₂

p1 =

• x : o₀
• y : o₁
• z : o₂

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origin

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torus_small *torus_small* - draws a smaller torus

torus_small <-- torus(p1,R1,R3)

p1 =

• x : o₀
• y : o₁
• z : o₂

R1 =

R3 =

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origin

R1 = Radius of curvature of the elbow

R3 = Inner radius of the elbow

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subtract2 - removes the smaller torus, making the large torus hollow by using p4 to select the large torus as the object to be subtracted from, and using p5 to select the smaller torus as the object to be subtracted.subtract2 - removes the left half of the smaller torus

subtract2 <-- subtractA(p4,p5)

p4 =

• x : o₀ + ElbowRadius(2*pipe_inrND) + outerraduis(2*pipe_inrND)
• y : o₁
• z : o₂

p5 =

• x : o₀ - ElbowRadius(2*pipe_inrND) - pipe_inr)innerD(ND,EN)/2
• y : o₁
• z : o₂

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box2- draws a box over the lower half of the remaining hollow torus

box2 <-- box(p6,p7)

p6 =

• x : o₀
• y : o₁ - ElbowRadius(2*pipe_inrND) - outerraduis(2*pipe_inrND) - zc
• z : o₂ - ConRadius(2*pipe_inrND)

p7 =

• x : o₀ + ElbowRadius(2*pipe_inrND) + outerraduis(2*pipe_inrND) + zc
• y : o₁
• z : o₂ + ConRadius(2*pipe_inr)

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• ND)

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subtract3 - removes a portion of the hollow elbow by using p9 to select the hollow torus as the object to be subtracted from, and using the origin to select the box as the object to be subtracted.subtract3 - removes the box that was drawn in the previous step
subtract3 <-- subtractD(p9,p1)

p9 =

• x : o₀
• y : o₁ + ElbowRadius(ND)
• z : o₂

p1 = origin

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outercylinder - draws a cylinder at the end of the elbow to form the outer surface of a socket

outercylinder <-- cylinderB(p9,R4,P10)

p9 =

• x : o₀
• y : o₁ + ElbowRadius(ND2*pipe_inr)
• z : o₂

R4 = Outer radius of the socket

p10 p1 =

• x : o₀ - SocketDepth(ND)
• y : o₁ + ElbowRadius(ND)
• z : o₂

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innercylinder outercylinder - draws a smaller cylinder at the end of the elbow to form the outer within the larger cylinder, forming the inner surface of a socket

outercylinder innercylinder <-- cylinderB(p9,R4R2,P10p10)

p9 =

• x : o₀
• y : o₁ + ElbowRadius(ND)
• z : o₂

R2 = Outer raduis of elbow

p10 =

• x : o₀ - SocketDepth(ND)
• y : o₁ + ElbowRadius(ND2*pipe_inr)
• z : o₂

R4 =

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subtract4 - removes the smaller cylinder, creating a hollow socket at the end of the elbow using p11 to select the region to subtract from, and using p12 and p13 to select the inner cylinder to be subtracted.

subtract4 <-- subtractH(p11,p12,p13)

p11 =

• x : o₀
• y : o₁ + ElbowRadius(ND) - ConRaduis(ND)
• z : o₂

p12 p10 =

• x : o₀ - SocketDepth(ND) - zc
• y : o₁ + ElbowRadius(ND) - outerraduis(2*pipe~inr~)
• y : o₁ + ElbowRadius(2*pipe_inr)
z : o₂
• ND)
• z : o₂

p13 =

• x : o₀ + zc
• y : o₁ + ElbowRadius(ND) + outerraduis(ND)
• z : o₂
  
  

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mirror - replicates the socket drawn onto the opposite end of the elbow by selecting the hollow cylinder using p14, then reflecting it over a mirror line created using p15 and p16 to give the slope and direction of the mirror line.

mirror <-- mirrorA(p14,p15,p16)

p14 =

• x : o₀ - SocketDepth(ND)
• y : o₁ + ElbowRadius(ND) - ConRaduis(ND)
• z : o₂

p15 =

• x : o₀
• y : o₁

p16 =

• x : o₀ + zc
• y : o₁ + zc

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bigunion - unites all the pieces drawn so the elbow will act as one unit, instead of three separate units.

bigunion <-- bigunion_elbow(p1,p17,p18,R1,R2)

p1 = origin

p17 =

• x : o₀ + ElbowRadius(ND)
• y : o₁ - SocketDepth( ND)
• z : o₂

p18 =

• x : o₀ - SocketDepth(ND)
• y : o₁ + ElbowRadius(ND)
• z : o₂

R1 = Radius of curvature of the elbow

R2 = Outer radius of the elbow