openscad/NopSCADlib
1
0
Fork 0
mirror of https://github.com/nophead/NopSCADlib.git synced 2025-08-09 00:46:32 +02:00
Code Issues Releases Wiki Activity

Added catenary curves.

Browse Source
This commit is contained in:
Chris Palmer
2020-09-19 12:11:54 +01:00
parent b11c5914b3
commit 1255e71271
4 changed files with 156 additions and 17 deletions
Download Patch File Download Diff File Expand all files Collapse all files

64
readme.md
View File

@@ -20,23 +20,23 @@ See [usage](docs/usage.md) for requirements, installation instructions and a usa
<th align="left"> Vitamins A-I </th><th align="left"> Vitamins J-Q </th><th align="left"> Vitamins R-Z </th><th align="left"> Printed </th><th align="left"> Utilities </th><th align="left"> Core Utilities </th></tr>
<tr><td> <a href = "#Axials">Axials</a> </td><td> <a href = "#Jack">Jack</a> </td><td> <a href = "#Rails">Rails</a> </td><td> <a href = "#Box">Box</a> </td><td> <a href = "#Annotation">Annotation</a> </td><td> <a href = "#BOM">BOM</a> </td></tr>
<tr><td> <a href = "#Ball_bearings">Ball_bearings</a> </td><td> <a href = "#KP_pillow_blocks">KP_pillow_blocks</a> </td><td> <a href = "#Ring_terminals">Ring_terminals</a> </td><td> <a href = "#Butt_box">Butt_box</a> </td><td> <a href = "#Bezier">Bezier</a> </td><td> <a href = "#Clip">Clip</a> </td></tr>
<tr><td> <a href = "#Batteries">Batteries</a> </td><td> <a href = "#LDRs">LDRs</a> </td><td> <a href = "#Rockers">Rockers</a> </td><td> <a href = "#Cable_grommets">Cable_grommets</a> </td><td> <a href = "#Dogbones">Dogbones</a> </td><td> <a href = "#Global">Global</a> </td></tr>
<tr><td> <a href = "#Belts">Belts</a> </td><td> <a href = "#LED_meters">LED_meters</a> </td><td> <a href = "#Rod">Rod</a> </td><td> <a href = "#Carriers">Carriers</a> </td><td> <a href = "#Fillet">Fillet</a> </td><td> <a href = "#Polyholes">Polyholes</a> </td></tr>
<tr><td> <a href = "#Blowers">Blowers</a> </td><td> <a href = "#LEDs">LEDs</a> </td><td> <a href = "#SCS_bearing_blocks">SCS_bearing_blocks</a> </td><td> <a href = "#Corner_block">Corner_block</a> </td><td> <a href = "#Gears">Gears</a> </td><td> <a href = "#Rounded_rectangle">Rounded_rectangle</a> </td></tr>
<tr><td> <a href = "#Bulldogs">Bulldogs</a> </td><td> <a href = "#Leadnuts">Leadnuts</a> </td><td> <a href = "#SK_brackets">SK_brackets</a> </td><td> <a href = "#Door_hinge">Door_hinge</a> </td><td> <a href = "#Hanging_hole">Hanging_hole</a> </td><td> <a href = "#Sphere">Sphere</a> </td></tr>
<tr><td> <a href = "#Buttons">Buttons</a> </td><td> <a href = "#Light_strips">Light_strips</a> </td><td> <a href = "#SMDs">SMDs</a> </td><td> <a href = "#Door_latch">Door_latch</a> </td><td> <a href = "#Horiholes">Horiholes</a> </td><td> <a href = "#Teardrops">Teardrops</a> </td></tr>
<tr><td> <a href = "#Cable_strips">Cable_strips</a> </td><td> <a href = "#Linear_bearings">Linear_bearings</a> </td><td> <a href = "#SSRs">SSRs</a> </td><td> <a href = "#Fan_guard">Fan_guard</a> </td><td> <a href = "#Layout">Layout</a> </td><td></td></tr>
<tr><td> <a href = "#Cameras">Cameras</a> </td><td> <a href = "#Magnets">Magnets</a> </td><td> <a href = "#Screws">Screws</a> </td><td> <a href = "#Fixing_block">Fixing_block</a> </td><td> <a href = "#Maths">Maths</a> </td><td></td></tr>
<tr><td> <a href = "#Circlips">Circlips</a> </td><td> <a href = "#Mains_sockets">Mains_sockets</a> </td><td> <a href = "#Sealing_strip">Sealing_strip</a> </td><td> <a href = "#Flat_hinge">Flat_hinge</a> </td><td> <a href = "#Offset">Offset</a> </td><td></td></tr>
<tr><td> <a href = "#Components">Components</a> </td><td> <a href = "#Microswitches">Microswitches</a> </td><td> <a href = "#Sheets">Sheets</a> </td><td> <a href = "#Foot">Foot</a> </td><td> <a href = "#Quadrant">Quadrant</a> </td><td></td></tr>
<tr><td> <a href = "#DIP">DIP</a> </td><td> <a href = "#Microview">Microview</a> </td><td> <a href = "#Spades">Spades</a> </td><td> <a href = "#Handle">Handle</a> </td><td> <a href = "#Round">Round</a> </td><td></td></tr>
<tr><td> <a href = "#D_connectors">D_connectors</a> </td><td> <a href = "#Modules">Modules</a> </td><td> <a href = "#Spools">Spools</a> </td><td> <a href = "#PCB_mount">PCB_mount</a> </td><td> <a href = "#Rounded_cylinder">Rounded_cylinder</a> </td><td></td></tr>
<tr><td> <a href = "#Displays">Displays</a> </td><td> <a href = "#Nuts">Nuts</a> </td><td> <a href = "#Springs">Springs</a> </td><td> <a href = "#PSU_shroud">PSU_shroud</a> </td><td> <a href = "#Rounded_polygon">Rounded_polygon</a> </td><td></td></tr>
<tr><td> <a href = "#Extrusion_brackets">Extrusion_brackets</a> </td><td> <a href = "#O_ring">O_ring</a> </td><td> <a href = "#Stepper_motors">Stepper_motors</a> </td><td> <a href = "#Printed_box">Printed_box</a> </td><td> <a href = "#Sector">Sector</a> </td><td></td></tr>
<tr><td> <a href = "#Extrusions">Extrusions</a> </td><td> <a href = "#Opengrab">Opengrab</a> </td><td> <a href = "#Swiss_clips">Swiss_clips</a> </td><td> <a href = "#Ribbon_clamp">Ribbon_clamp</a> </td><td> <a href = "#Sweep">Sweep</a> </td><td></td></tr>
<tr><td> <a href = "#Fans">Fans</a> </td><td> <a href = "#PCB">PCB</a> </td><td> <a href = "#Toggles">Toggles</a> </td><td> <a href = "#SSR_shroud">SSR_shroud</a> </td><td> <a href = "#Thread">Thread</a> </td><td></td></tr>
<tr><td> <a href = "#Fuseholder">Fuseholder</a> </td><td> <a href = "#PCBs">PCBs</a> </td><td> <a href = "#Transformers">Transformers</a> </td><td> <a href = "#Screw_knob">Screw_knob</a> </td><td> <a href = "#Tube">Tube</a> </td><td></td></tr>
<tr><td> <a href = "#Geared_steppers">Geared_steppers</a> </td><td> <a href = "#PSUs">PSUs</a> </td><td> <a href = "#Tubings">Tubings</a> </td><td> <a href = "#Socket_box">Socket_box</a> </td><td></td><td></td></tr>
<tr><td> <a href = "#Batteries">Batteries</a> </td><td> <a href = "#LDRs">LDRs</a> </td><td> <a href = "#Rockers">Rockers</a> </td><td> <a href = "#Cable_grommets">Cable_grommets</a> </td><td> <a href = "#Catenary">Catenary</a> </td><td> <a href = "#Global">Global</a> </td></tr>
<tr><td> <a href = "#Belts">Belts</a> </td><td> <a href = "#LED_meters">LED_meters</a> </td><td> <a href = "#Rod">Rod</a> </td><td> <a href = "#Carriers">Carriers</a> </td><td> <a href = "#Dogbones">Dogbones</a> </td><td> <a href = "#Polyholes">Polyholes</a> </td></tr>
<tr><td> <a href = "#Blowers">Blowers</a> </td><td> <a href = "#LEDs">LEDs</a> </td><td> <a href = "#SCS_bearing_blocks">SCS_bearing_blocks</a> </td><td> <a href = "#Corner_block">Corner_block</a> </td><td> <a href = "#Fillet">Fillet</a> </td><td> <a href = "#Rounded_rectangle">Rounded_rectangle</a> </td></tr>
<tr><td> <a href = "#Bulldogs">Bulldogs</a> </td><td> <a href = "#Leadnuts">Leadnuts</a> </td><td> <a href = "#SK_brackets">SK_brackets</a> </td><td> <a href = "#Door_hinge">Door_hinge</a> </td><td> <a href = "#Gears">Gears</a> </td><td> <a href = "#Sphere">Sphere</a> </td></tr>
<tr><td> <a href = "#Buttons">Buttons</a> </td><td> <a href = "#Light_strips">Light_strips</a> </td><td> <a href = "#SMDs">SMDs</a> </td><td> <a href = "#Door_latch">Door_latch</a> </td><td> <a href = "#Hanging_hole">Hanging_hole</a> </td><td> <a href = "#Teardrops">Teardrops</a> </td></tr>
<tr><td> <a href = "#Cable_strips">Cable_strips</a> </td><td> <a href = "#Linear_bearings">Linear_bearings</a> </td><td> <a href = "#SSRs">SSRs</a> </td><td> <a href = "#Fan_guard">Fan_guard</a> </td><td> <a href = "#Horiholes">Horiholes</a> </td><td></td></tr>
<tr><td> <a href = "#Cameras">Cameras</a> </td><td> <a href = "#Magnets">Magnets</a> </td><td> <a href = "#Screws">Screws</a> </td><td> <a href = "#Fixing_block">Fixing_block</a> </td><td> <a href = "#Layout">Layout</a> </td><td></td></tr>
<tr><td> <a href = "#Circlips">Circlips</a> </td><td> <a href = "#Mains_sockets">Mains_sockets</a> </td><td> <a href = "#Sealing_strip">Sealing_strip</a> </td><td> <a href = "#Flat_hinge">Flat_hinge</a> </td><td> <a href = "#Maths">Maths</a> </td><td></td></tr>
<tr><td> <a href = "#Components">Components</a> </td><td> <a href = "#Microswitches">Microswitches</a> </td><td> <a href = "#Sheets">Sheets</a> </td><td> <a href = "#Foot">Foot</a> </td><td> <a href = "#Offset">Offset</a> </td><td></td></tr>
<tr><td> <a href = "#DIP">DIP</a> </td><td> <a href = "#Microview">Microview</a> </td><td> <a href = "#Spades">Spades</a> </td><td> <a href = "#Handle">Handle</a> </td><td> <a href = "#Quadrant">Quadrant</a> </td><td></td></tr>
<tr><td> <a href = "#D_connectors">D_connectors</a> </td><td> <a href = "#Modules">Modules</a> </td><td> <a href = "#Spools">Spools</a> </td><td> <a href = "#PCB_mount">PCB_mount</a> </td><td> <a href = "#Round">Round</a> </td><td></td></tr>
<tr><td> <a href = "#Displays">Displays</a> </td><td> <a href = "#Nuts">Nuts</a> </td><td> <a href = "#Springs">Springs</a> </td><td> <a href = "#PSU_shroud">PSU_shroud</a> </td><td> <a href = "#Rounded_cylinder">Rounded_cylinder</a> </td><td></td></tr>
<tr><td> <a href = "#Extrusion_brackets">Extrusion_brackets</a> </td><td> <a href = "#O_ring">O_ring</a> </td><td> <a href = "#Stepper_motors">Stepper_motors</a> </td><td> <a href = "#Printed_box">Printed_box</a> </td><td> <a href = "#Rounded_polygon">Rounded_polygon</a> </td><td></td></tr>
<tr><td> <a href = "#Extrusions">Extrusions</a> </td><td> <a href = "#Opengrab">Opengrab</a> </td><td> <a href = "#Swiss_clips">Swiss_clips</a> </td><td> <a href = "#Ribbon_clamp">Ribbon_clamp</a> </td><td> <a href = "#Sector">Sector</a> </td><td></td></tr>
<tr><td> <a href = "#Fans">Fans</a> </td><td> <a href = "#PCB">PCB</a> </td><td> <a href = "#Toggles">Toggles</a> </td><td> <a href = "#SSR_shroud">SSR_shroud</a> </td><td> <a href = "#Sweep">Sweep</a> </td><td></td></tr>
<tr><td> <a href = "#Fuseholder">Fuseholder</a> </td><td> <a href = "#PCBs">PCBs</a> </td><td> <a href = "#Transformers">Transformers</a> </td><td> <a href = "#Screw_knob">Screw_knob</a> </td><td> <a href = "#Thread">Thread</a> </td><td></td></tr>
<tr><td> <a href = "#Geared_steppers">Geared_steppers</a> </td><td> <a href = "#PSUs">PSUs</a> </td><td> <a href = "#Tubings">Tubings</a> </td><td> <a href = "#Socket_box">Socket_box</a> </td><td> <a href = "#Tube">Tube</a> </td><td></td></tr>
<tr><td> <a href = "#Green_terminals">Green_terminals</a> </td><td> <a href = "#Panel_meters">Panel_meters</a> </td><td> <a href = "#Variacs">Variacs</a> </td><td> <a href = "#Strap_handle">Strap_handle</a> </td><td></td><td></td></tr>
<tr><td> <a href = "#Hot_ends">Hot_ends</a> </td><td> <a href = "#Pillars">Pillars</a> </td><td> <a href = "#Veroboard">Veroboard</a> </td><td></td><td></td><td></td></tr>
<tr><td> <a href = "#Hygrometer">Hygrometer</a> </td><td> <a href = "#Pin_headers">Pin_headers</a> </td><td> <a href = "#Washers">Washers</a> </td><td></td><td></td><td></td></tr>
@@ -5245,6 +5245,36 @@ Bezier curves and function to get and adjust the length or minimum z point.
![bezier](tests/png/bezier.png)
<a href="#top">Top</a>
---
<a name="Catenary"></a>
## Catenary
Catenary curve to model hanging wires, etc.
Although the equation of the curve is simply ```y = a cosh(x / a)``` there is no explicit formula to calculate the constant ```a``` or the range of ```x``` given the
length of the cable and the end point coordinates. See <https://en.wikipedia.org/wiki/Catenary#Determining_parameters>. The Newton-Raphson method is used to find
```a``` numerically, see <https://en.wikipedia.org/wiki/Newton%27s_method>.
The coordinates of the lowest point on the curve can be retrieved by calling ```catenary_points()``` with ```steps``` equal to zero.
[utils/catenary.scad](utils/catenary.scad) Implementation.
[tests/catenary.scad](tests/catenary.scad) Code for this example.
### Functions
| Function | Description |
|:--- |:--- |
| ```catenary(t, a)``` | Parametric catenary function linear along the length of the curve. |
| ```catenary_ds_by_da(d, a)``` | First derivative of the length with respect to ```a```. |
| ```catenary_find_a(d, l, a = 1)``` | Find the catenary constant ```a```, given half the horizontal span and the length. |
| ```catenary_points(l, x, y, steps = 100)``` | Returns a list of 2D points on the curve that goes from the origin to ```(x,y)``` and has length ```l```. |
| ```catenary_s(d, a)``` | Length of a symmetric catenary with width ```2d```. |
![catenary](tests/png/catenary.png)
<a href="#top">Top</a>
---