Added tesrdrop_minus() and horicylinder().

readme.md

@@ -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>
@@ -2332,14 +2332,14 @@ PCBs and perfboard with optional components. The shape can be a rectangle with o
 |   1 | ```pcb(EnviroPlus)``` |  Enviro+ |
 |   1 | ```pcb(ExtruderPCB)``` |  Extruder connection PCB |
 |   1 | ```pcb(Keyes5p1)``` |  Keyes5.1 Arduino Uno expansion board |
+|   1 | ```pcb(MP1584EN)``` |  MP1584EN 3A buck converter |
 |   1 | ```pcb(MT3608)``` |  MT3608 boost converter module |
-|   1 | ```pcb(Melzi)``` |  Melzi electronics |
-|   5 |  |  Micro SD card |
+|   4 |  |  Micro SD card |
 |   1 | ```molex_254(2)``` |  Molex KK header 2 way |
 |   1 | ```molex_254(3)``` |  Molex KK header 3 way |
 |  16 | ```nut(M2_nut, nyloc = true)``` |  Nut M2 x 1.6mm nyloc |
 |  34 | ```nut(M2p5_nut, nyloc = true)``` |  Nut M2.5 x 2.2mm nyloc |
-|  16 | ```nut(M3_nut, nyloc = true)``` |  Nut M3 x 2.4mm nyloc |
+|  12 | ```nut(M3_nut, nyloc = true)``` |  Nut M3 x 2.4mm nyloc |
 |  12 | ```nut(M4_nut, nyloc = true)``` |  Nut M4 x 3.2mm nyloc |
 |   1 | ```pcb(PI_IO)``` |  PI_IO V2 |
 |   1 | ```pcb(PSU12V1A)``` |  PSU 12V 1A |
@@ -2355,24 +2355,21 @@ PCBs and perfboard with optional components. The shape can be a rectangle with o
 |   1 | ```pcb(RPI0)``` |  Raspberry Pi Zero |
 |  12 | ```screw(M2_cap_screw, 16)``` |  Screw M2 cap x 16mm |
 |   4 | ```screw(M2_cap_screw, 20)``` |  Screw M2 cap x 20mm |
-|   2 | ```screw(M2p5_cap_screw, 16)``` |  Screw M2.5 cap x 16mm |
-|   4 | ```screw(M2p5_cap_screw, 20)``` |  Screw M2.5 cap x 20mm |
-|   4 | ```screw(M2p5_cap_screw, 25)``` |  Screw M2.5 cap x 25mm |
+|   2 | ```screw(M2p5_cap_screw, 20)``` |  Screw M2.5 cap x 20mm |
+|   8 | ```screw(M2p5_cap_screw, 25)``` |  Screw M2.5 cap x 25mm |
 |   8 | ```screw(M2p5_cap_screw, 30)``` |  Screw M2.5 cap x 30mm |
 |   4 | ```screw(M2p5_pan_screw, 20)``` |  Screw M2.5 pan x 20mm |
 |  12 | ```screw(M2p5_pan_screw, 25)``` |  Screw M2.5 pan x 25mm |
 |   4 | ```screw(M3_cap_screw, 16)``` |  Screw M3 cap x 16mm |
 |   8 | ```screw(M3_cap_screw, 30)``` |  Screw M3 cap x 30mm |
-|   4 | ```screw(M3_cap_screw, 35)``` |  Screw M3 cap x 35mm |
 |  12 | ```screw(M4_cap_screw, 35)``` |  Screw M4 cap x 35mm |
 |   1 | ```pcb(TP4056)``` |  TP4056 Li-lon Battery charger module |
 |   3 | ```terminal_35(2)``` |  Terminal block 2 way 3.5mm |
 |   2 | ```green_terminal(gt_2p54, 4)``` |  Terminal block 4 way 0.1" |
-|   1 |  |  USB A to Mini B lead |
 |   1 | ```pcb(WD2002SJ)``` |  WD2002SJ Buck Boost DC-DC converter |
 |  16 | ```washer(M2_washer)``` |  Washer  M2 x 5mm x 0.3mm |
 |  34 | ```washer(M2p5_washer)``` |  Washer  M2.5 x 5.9mm x 0.5mm |
-|  16 | ```washer(M3_washer)``` |  Washer  M3 x 7mm x 0.5mm |
+|  12 | ```washer(M3_washer)``` |  Washer  M3 x 7mm x 0.5mm |
 |  12 | ```washer(M4_washer)``` |  Washer  M4 x 9mm x 0.8mm |
 |   1 | ```pcb(ZC_A0591)``` |  ZC-A0591 ULN2003 driver PCB |
 
@@ -2383,22 +2380,21 @@ PCBs and perfboard with optional components. The shape can be a rectangle with o
 |   4 | pcb_spacer2070.stl |
 |   4 | pcb_spacer2080.stl |
 |   4 | pcb_spacer2090.stl |
-|   4 | pcb_spacer25100.stl |
 |   4 | pcb_spacer25110.stl |
 |   4 | pcb_spacer25120.stl |
-|   4 | pcb_spacer25130_2.stl |
+|   4 | pcb_spacer25130.stl |
 |   4 | pcb_spacer25140_2.stl |
 |   4 | pcb_spacer25150_2.stl |
-|   4 | pcb_spacer25180.stl |
+|   4 | pcb_spacer25160_2.stl |
 |   4 | pcb_spacer25190.stl |
-|   2 | pcb_spacer2570.stl |
-|   4 | pcb_spacer30160.stl |
+|   4 | pcb_spacer25200.stl |
+|   2 | pcb_spacer2580.stl |
 |   4 | pcb_spacer30170.stl |
-|   4 | pcb_spacer30230.stl |
+|   4 | pcb_spacer30180.stl |
 |   4 | pcb_spacer3050.stl |
-|   4 | pcb_spacer40200.stl |
 |   4 | pcb_spacer40210.stl |
 |   4 | pcb_spacer40220.stl |
+|   4 | pcb_spacer40230.stl |
 
 
 <a href="#top">Top</a>
@@ -5245,6 +5241,36 @@ 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, best_e = inf, best_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>
 
 ---
@@ -5361,6 +5387,8 @@ Method to print holes in mid air. See <https://hydraraptor.blogspot.com/2014/03/
 ## Horiholes
 Utilities for depicting the staircase slicing of horizontal holes made with [`teardrop_plus()`](#teardrops), see <https://hydraraptor.blogspot.com/2020/07/horiholes-2.html>
 
+horicylinder() makes cylinders that fit inside a round hole. Layers that are less than 2 filaments wide and layers that need more than a 45 degree overhang are ommitted.
+
 
 [utils/horiholes.scad](utils/horiholes.scad) Implementation.
 
@@ -5369,11 +5397,13 @@ Utilities for depicting the staircase slicing of horizontal holes made with [`te
 ### Functions
 | Function | Description |
 |:--- |:--- |
+| ```teardrop_minus_x(r, y, h)``` | Calculate the ordinate of a compensated teardrop given y and layer height. |
 | ```teardrop_plus_x(r, y, h)``` | Calculate the ordinate of a compensated teardrop given y and layer height. |
 
 ### Modules
 | Module | Description |
 |:--- |:--- |
+| ```horicylinder(r, z, h = 0, center = true)``` | For making horizontal cylinders that don't need support material and are correct dimensions |
 | ```horihole(r, z, h = 0, center = true)``` | For making horizontal holes that don't need support material and are correct dimensions |
 
 ![horiholes](tests/png/horiholes.png)
@@ -5420,7 +5450,14 @@ Maths utilities for manipulating vectors and matrices.
 | Function | Description |
 |:--- |:--- |
 | ```angle_between(v1, v2)``` | Return the angle between two vectors |
+| ```argcosh(x)``` | inverse hyperbolic cosine |
+| ```argcoth(x)``` | inverse hyperbolic cotangent |
+| ```argsinh(x)``` | inverse hyperbolic sine |
+| ```argtanh(x)``` | inverse hyperbolic tangent |
 | ```augment(m)``` | Augment a matrix by adding an identity matrix to the right |
+| ```circle_intersect(c1, r1, c2, r2)``` | Calculate one point where two circles in the X-Z plane intersect, clockwise around c1 |
+| ```cosh(x)``` | hyperbolic cosine |
+| ```coth(x)``` | hyperbolic cotangent |
 | ```degrees(radians)``` | Convert degrees to radians |
 | ```euler(R)``` | Convert a rotation matrix to a Euler rotation vector. |
 | ```identity(n, x = 1)``` | Construct an arbitrary size identity matrix |
@@ -5433,9 +5470,11 @@ Maths utilities for manipulating vectors and matrices.
 | ```rotate(a, v)``` | Generate a 4x4 rotation matrix, ```a``` can be a vector of three angles or a single angle around ```z```, or around axis ```v``` |
 | ```rowswap(m, i, j)``` | Swap two rows of a matrix |
 | ```scale(v)``` |  Generate a 4x4 matrix that scales by ```v```, which can be a vector of xyz factors or a scalar to scale all axes equally |
+| ```sinh(x)``` | hyperbolic sine |
 | ```solve(m, i = 0, j = 0)``` | Solve each row ensuring diagonal is not zero |
 | ```solve_row(m, i)``` | Make diagonal one by dividing the row by it and subtract from other rows to make column zero |
 | ```sqr(x)``` | Square x |
+| ```tanh(x)``` | hyperbolic tangent |
 | ```transform(v, m)``` | Apply 4x4 transform to a 3 vector by extending it and cropping it again |
 | ```transform_points(path, m)``` | Apply transform to a path |
 | ```translate(v)``` | Generate a 4x4 translation matrix, ```v``` can be ```[x, y]```, ```[x, y, z]``` or ```z``` |

tests/catenary.scad

@@ -0,0 +1,56 @@
+//
+// NopSCADlib Copyright Chris Palmer 2020
+// nop.head@gmail.com
+// hydraraptor.blogspot.com
+//
+// This file is part of NopSCADlib.
+//
+// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
+// GNU General Public License as published by the Free Software Foundation, either version 3 of
+// the License, or (at your option) any later version.
+//
+// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
+// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+// See the GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along with NopSCADlib.
+// If not, see <https://www.gnu.org/licenses/>.
+//
+l = 250; // [1: 1000]
+x = 200; // [1: 1000]
+y = 50; //[-500 : 500]
+
+include <../utils/core/core.scad>
+use <../utils/catenary.scad>
+use <../utils/sweep.scad>
+use <../utils/annotation.scad>
+
+module catenaries() {
+    //
+    // catenary curve path from control points
+    //
+    curve = [for(p = catenary_points(l, x, y)) [p.x, p.y, 0]];
+    //
+    // Draw the curve
+    //
+    r = 0.5;
+    sweep(curve, circle_points(r, $fn = 64));
+    //
+    // Minimum Z
+    //
+    min_z = catenary_points(l, x, y, 0);
+
+    color("blue") {
+        translate([min_z.x, min_z.y + r])
+            rotate([-90, 0, 0])
+                arrow();
+
+        translate([min_z.x, min_z.y - r])
+            rotate([90, 0, 0])
+                arrow();
+    }
+}
+
+if($preview)
+    rotate(is_undef($bom) ? 0 : [70, 0, 315])
+        catenaries();

tests/horiholes.scad

@@ -69,9 +69,13 @@ module horiholes() {
             color(silver)
                 cylinder(r = $r, h = eps, center = true, $fn = 360);
 
+    hole_positions()
+        color("blue")
+            horicylinder(r = $r, z = $z, h = 2 * eps, center = true, $fn = 360);
+
     hole_positions()
         color("red")
-            linear_extrude(2 * eps, center = true)
+            linear_extrude(3 * eps, center = true)
                 intersection() {
                     difference() {
                         square(8, center = true);

tests/maths.scad

@@ -69,6 +69,33 @@ module maths() {
     // Test Euler
     //
     assert(euler(rotate(r)) == r, "euler() failed");
+    //
+    // Circle intersect
+    //
+    r1 = 10;
+    c1 = [50, 0, 10];
+    r2 = 20;
+    c2 = [67, 0, 0];
+    p1 = circle_intersect(c1, r1, c2, r2);
+    p2 = circle_intersect(c2, r2, c1, r1);
+
+    rotate(90) {
+        color(grey(90))
+            translate(c1) rotate([90, 0, 0]) cylinder(r = r1, h = 4 * eps, center = true);
+
+        color(grey(80))
+            translate(c2) rotate([90, 0, 0]) cylinder(r = r2, h = eps, center = true);
+
+        color("red")
+            translate(p1) rotate([90, 0, 0]) cylinder(r = 0.1, h = 6 * eps, center = true);
+
+        color("blue")
+            translate(p2) rotate([90, 0, 0]) cylinder(r = 0.1, h = 6 * eps, center = true);
+
+        translate(p1) arrow();
+
+        translate(p2) vflip() arrow();
+    }
 }
 
 rotate(45)

utils/catenary.scad

@@ -0,0 +1,52 @@
+//
+// NopSCADlib Copyright Chris Palmer 2020
+// nop.head@gmail.com
+// hydraraptor.blogspot.com
+//
+// This file is part of NopSCADlib.
+//
+// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
+// GNU General Public License as published by the Free Software Foundation, either version 3 of
+// the License, or (at your option) any later version.
+//
+// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
+// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+// See the GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along with NopSCADlib.
+// If not, see <https://www.gnu.org/licenses/>.
+//
+
+//
+//! 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.
+//
+include <core/core.scad>
+use <maths.scad>
+
+function catenary(t, a) = let(u = argsinh(t)) a * [u, cosh(u)]; //! Parametric catenary function linear along the length of the curve.
+function catenary_s(d, a) = 2 * a * sinh(d / a); //! Length of a symmetric catenary with width ```2d```.
+function catenary_ds_by_da(d, a) = 2 * sinh(d / a) - 2 * d / a * cosh(d / a); //! First derivative of the length with respect to ```a```.
+
+function catenary_find_a(d, l, a = 1, best_e = inf, best_a = 1) =  //! Find the catenary constant ```a```, given half the horizontal span and the length.
+     assert(l > 2 * d, "Not long enough to span the gap") assert(d) let(error = abs(catenary_s(d, a) - l))
+     error >= best_e && error < 0.0001 ? best_a
+                                       : catenary_find_a(d, l, max(a - (catenary_s(d, a) - l) / catenary_ds_by_da(d, a), d / argsinh(1e99)), error, a);
+
+function 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```.
+    let(
+        d = x / 2,
+        a = catenary_find_a(d, sqrt(sqr(l) - sqr(y))),   // Find a to get the correct length
+        offset = argsinh(y / catenary_s(d, a)),
+        t0 = sinh(-d / a + offset),
+        t1 = sinh( d / a + offset),
+        h = a * cosh(-d / a + offset) - a,
+        lowest = offset > d / a ? [0, 0] : offset < -d / a ? [x, y] : [d - offset * a, -h],
+        p0 = catenary(t0, a)
+    )
+    steps ? [for(t = [t0 : (t1 - t0) / steps : t1]) catenary(t, a) - p0] : lowest;

utils/horiholes.scad

@@ -19,6 +19,8 @@
 
 //
 //! Utilities for depicting the staircase slicing of horizontal holes made with [`teardrop_plus()`](#teardrops), see <https://hydraraptor.blogspot.com/2020/07/horiholes-2.html>
+//!
+//! horicylinder() makes cylinders that fit inside a round hole. Layers that are less than 2 filaments wide and layers that need more than a 45 degree overhang are ommitted.
 //
 include <../utils/core/core.scad>
 
@@ -53,3 +55,29 @@ module horihole(r, z, h = 0, center = true) { //! For making horizontal holes th
                         }
              }
 }
+
+function teardrop_minus_x(r, y, h) = //! Calculate the ordinate of a compensated teardrop given y and layer height.
+    let(fr = h / 2,
+        hpot = r - fr,
+        x2 = sqr(hpot) - sqr(y),
+        x = x2 > 0 ? sqrt(x2) : 0,
+        X = y >= -hpot / sqrt(2) ? x + fr : 0
+    )
+    X >= extrusion_width ? X : 0;
+
+module horicylinder(r, z, h = 0, center = true) { //! For making horizontal cylinders that don't need support material and are correct dimensions
+    bot_layer = floor((z - r) / layer_height);
+    top_layer = ceil((z + r) / layer_height);
+    render(convexity = 5)
+        extrude_if(h, center)
+            for(i = [bot_layer : top_layer]) {
+                Z = i * layer_height;
+                y = Z - z + layer_height / 2;
+                x = teardrop_minus_x(r, y, layer_height);
+                if(x >= extrusion_width)
+                    hull()
+                        for(end = [-1, 1])
+                            translate([end * (x - layer_height / 2), y])
+                                circle(d = layer_height, $fn = 32);
+             }
+}

utils/maths.scad

@@ -24,6 +24,14 @@ function sqr(x) = x * x;                        //! Square x
 function radians(degrees) = degrees * PI / 180; //! Convert radians to degrees
 function degrees(radians) = radians * 180 / PI; //! Convert degrees to radians
 
+function sinh(x) = (exp(x) - exp(-x)) / 2;      //! hyperbolic sine
+function cosh(x) = (exp(x) + exp(-x)) / 2;      //! hyperbolic cosine
+function tanh(x) = sinh(x) / cosh(x);           //! hyperbolic tangent
+function coth(x) = cosh(x) / sinh(x);           //! hyperbolic cotangent
+function argsinh(x) = ln(x + sqrt(sqr(x) + 1)); //! inverse hyperbolic sine
+function argcosh(x) = ln(x + sqrt(sqr(x) - 1)); //! inverse hyperbolic cosine
+function argtanh(x) = ln((1 + x) / (1 - x)) / 2;//! inverse hyperbolic tangent
+function argcoth(x) = ln((x + 1) / (x - 1)) / 2;//! inverse hyperbolic cotangent
 
 function translate(v) = let(u = is_list(v) ? len(v) == 2 ? [v.x, v.y, 0] //! Generate a 4x4 translation matrix, ```v``` can be ```[x, y]```, ```[x, y, z]``` or ```z```
                                                          : v
@@ -138,3 +146,10 @@ function invert(m) = let(n =len(m), m = solve(augment(m))) [ //! Invert a matrix
              each m[i][j]
     ]
 ];
+
+function circle_intersect(c1, r1, c2, r2) =     //! Calculate one point where two circles in the X-Z plane intersect, clockwise around c1
+    let(
+        v = c1 - c2,                            // Line between centres
+        d = norm(v),                            // Distance between centres
+        a = atan2(v.z, v.x) - acos((sqr(d) + sqr(r2) - sqr(r1)) / (2 * d * r2)) // Cosine rule to find angle from c2
+     ) c2 + r2 * [cos(a), 0, sin(a)];           // Point on second circle

vitamins/component.scad

@@ -161,13 +161,13 @@ module al_clad_resistor(type, value, leads = true) { //! Draw an aluminium clad
                 }
         linear_extrude(thickness)
             difference() {
-                for(end = [-1, 1])
-                    translate([end * (length - tab) / 2, end * (width - width / 2) / 2])
-                        square([tab, width / 2], center = true);
+                union()
+                    for(end = [-1, 1])
+                        translate([end * (length - tab) / 2, end * (width - width / 2) / 2])
+                            square([tab, width / 2], center = true);
 
                 al_clad_resistor_hole_positions(type)
                     circle(d = al_clad_hole(type));
-
             }
         if(leads) {
             translate_z(height / 2)

vitamins/insert.scad

@@ -137,19 +137,26 @@ module insert_lug(insert, wall, counter_bore = 0, extension = 0, corner_r = 0, f
     boss_h = insert_hole_length(insert);
     boss_h2 = boss_h + counter_bore;
 
-    module shape()
-        intersection() {
+    module shape() {
+        module _shape()
             hull() {
                 circle(boss_r);
 
                 translate([boss_r + extension - eps, 0])
                     square([eps, 2 * boss_r], center = true);
             }
-            if(corner_r)
+
+        if(corner_r)
+            intersection() {
+                _shape();
+
                 translate([boss_r + extension - corner_r, 0])
                     rotate(-45)
                         quadrant(w = 100, r = corner_r - eps, center = true);
-        }
+            }
+        else
+            _shape();
+    }
 
     translate_z(-boss_h)
         linear_extrude(boss_h)

vitamins/jhead.scad

@@ -179,23 +179,27 @@ module jhead_hot_end_assembly(type, filament, naked = false) { //! Assembly with
     //
     // heater block
     //
-    rotate(90)
-        translate([-nozzle_x(heater), 0, inset - insulator_length - heater_height(heater) / 2]) {
-            intersection() {
-                group() {
-                    translate([resistor_x(heater), -exploded() * 15, 0])
-                        rotate([90, 0, 0])
-                             sleeved_resistor(resistor, PTFE20, bare = -10);
+    module heater_components() {
+        translate([resistor_x(heater), -exploded() * 15, 0])
+            rotate([90, 0, 0])
+                 sleeved_resistor(resistor, PTFE20, bare = -10);
+
+        translate([-heater_length(heater) / 2 + resistor_length(thermistor) / 2 - exploded() * 10, thermistor_y(heater), 0])
+            rotate([90, 0, -90])
+                 sleeved_resistor(thermistor, PTFE07, heatshrink = HSHRNK16);
+    }
+
+    rotate(90)
+        translate([-nozzle_x(heater), 0, inset - insulator_length - heater_height(heater) / 2])
+            if(exploded())
+                heater_components();
+            else
+                intersection() {
+                    heater_components();
 
-                    translate([-heater_length(heater) / 2 + resistor_length(thermistor) / 2 - exploded() * 10, thermistor_y(heater), 0])
-                        rotate([90, 0, -90])
-                             sleeved_resistor(thermistor, PTFE07, heatshrink = HSHRNK16);
-                }
-                if(!exploded())
                     if(naked)
                         color("grey") cylinder(r = 12, h = 100, center = true);
                     else
                         cube(1, true);             // hide the wires when not exploded
-            }
-    }
+                }
 }

vitamins/panel_meter.scad

@@ -77,7 +77,6 @@ module panel_meter(type) { //! Draw panel mounted LCD meter module
     tab_z = pmeter_tab_z(type);
     pcb = pmeter_pcb(type);
     ap2 = pmeter_inner_ap(type);
-    pcb_h = pmeter_pcb_h(type) - bezel.z;
     buttons = pmeter_buttons(type);
 
     color("#94A7AB")
@@ -146,15 +145,16 @@ module panel_meter(type) { //! Draw panel mounted LCD meter module
                     translate(pmeter_inner_ap_o(type))
                         square([ap2.x, ap2.y], center = true);
                 }
-    if(pcb)
+    if(pcb) {
         vflip()
             translate_z(h - pcb_thickness(pcb) - pmeter_pcb_z(type))
                 pcb(pcb);
 
-    if(pcb_h > 0)
-        %translate_z(-pcb_h / 2 - eps)
-            cube([size.x - 2 * t - eps, size.y - 2 * t - eps, pcb_h], center = true);
-
+        pcb_h = pmeter_pcb_h(type) - bezel.z;
+        if(pcb_h > 0)
+            %translate_z(-pcb_h / 2 - eps)
+                cube([size.x - 2 * t - eps, size.y - 2 * t - eps, pcb_h], center = true);
+    }
     if(buttons)
         for(b = buttons)
             panel_meter_button(b);

vitamins/panel_meters.scad

@@ -44,7 +44,7 @@ DSP5005   = ["DSP5005", "Ruideng DSP5005 Power supply module",                [7
 DSN_VC288PCB = ["", "", 41, 21, 1, 0, 0, 0, "green", false, [], [[ 5,  -3,   0, "jst_xh", 3], ], []];
 
 DSN_VC288 = ["DSN_VC288","DSN-VC288 DC 100V 10A Voltmeter ammeter",            [45.3, 26,   17.4], [47.8, 28.8, 2.5], 0,   [1, 1.8], [36, 18, 2.5], [],            0, 2,
-              [], 0, DSN_VC288PCB, 5];
+              [], 0, DSN_VC288PCB, 5, 0];
 
 panel_meters = [DSN_VC288, PZEM021, PZEM001, DSP5005];
 

vitamins/pcbs.scad

@@ -385,6 +385,11 @@ WD2002SJ = ["WD2002SJ", "WD2002SJ Buck Boost DC-DC converter", 78, 47, 1.6, 0, 3
     ],
     []];
 
+MP1584EN = ["MP1584EN", "MP1584EN 3A buck converter", 22, 17, 1.2, 0, 1, [2, 2], "green", false,
+    [[1.75, 1.75], [1.75, -1.75], [-1.75, 1.75], [-1.75, -1.75], [-1.75, -4.4], [-1.75, 4.48], [1.75, -4.4], [1.75, 4.4]],
+    []
+];
+
 PERF80x20 = ["PERF80x20", "Perfboard 80 x 20mm", 80, 20, 1.6, 0, 2.3, 0, "green", true, [[2,2],[-2,2],[2,-2],[-2,-2]], [], [], [5.87, 3.49]];
 
 PERF70x50 = ["PERF70x50", "Perfboard 70 x 50mm", 70, 50, 1.6, 0, 2.3, 0, "green", true, [[2,2],[-2,2],[2,-2],[-2,-2]], [], [], [5.87, 3.49]];
@@ -410,7 +415,7 @@ RAMPSEndstop = ["RAMPSEndstop", "RAMPS Endstop Switch",
     []];
 
 
-pcbs = [TP4056, MT3608, RAMPSEndstop, ExtruderPCB, PI_IO, ZC_A0591, RPI0, EnviroPlus, ArduinoUno3, ArduinoLeonardo, Keyes5p1, PSU12V1A, WD2002SJ, RPI3, RPI4, DuetE, Duex2, Duex5, Melzi];
+pcbs = [MP1584EN, TP4056, MT3608, RAMPSEndstop, ExtruderPCB, PI_IO, ZC_A0591, RPI0, EnviroPlus, ArduinoUno3, ArduinoLeonardo, Keyes5p1, PSU12V1A, WD2002SJ, RPI3, RPI4, DuetE, Duex2, Duex5];
 
 perfboards = [PERF74x51, PERF70x50, PERF60x40, PERF70x30, PERF80x20];
 

vitamins/smd.scad

@@ -62,9 +62,10 @@ module smd_led(type, colour, cutout) { //! Draw an SMD LED with specified ```col
                 intersection() {
                     square([size.x, size.y], center = true);
 
-                    for(end = [-1, 1])
-                        translate([end * size.x / 2, 0])
-                            ring(or = r, ir = r / 2);
+                    union()
+                        for(end = [-1, 1])
+                            translate([end * size.x / 2, 0])
+                                ring(or = r, ir = r / 2);
                 }
 
         color(colour, 0.9)

vitamins/stepper_motor.scad

@@ -89,7 +89,7 @@ module NEMA(type, shaft_angle = 0) { //! Draw specified NEMA stepper motor
         tube(or = boss_rad, ir =  shaft_rad + 2, h = boss_height * 2); // raised boss
 
         linear_extrude(eps)
-            cap_shape(true);
+            cap_shape(1);
     }
 
     color(stepper_cap_colour)                                       // aluminium end caps