Make Helix Shape in occQt

[eryar]

Make Helix Shape in occQt

1.Introduction

OpenCASCADE does not provide helix curve directly, but you can build a helix curve by the pcurve of a surface(curve on surface). When you understand the pcurve of a surface, you can make a helix curve easily.

To try the idea quickly, Let's first make a helix by Tcl in Draw Test Harness, then translate the Tcl script to OpenCASCADE C++ code for occQt.

2.Helix Equation

Helix shape is very common shapes, such as the spiral staircase, drill, .etc. The helix curve parametric equation as follows:
And the Helix curve is like this:

But OpenCASCADE does not support the parametric equation like this, of course you can inherit Geom_Curve to make a Geom_HelixCurve, maybe the method is a little complicated. You can also use the pcurve to make the helix easily. Use pcurve on different surface will produce very interesting curves, I will try this in the Draw Test Harness by Tcl first.

3. Make Helix Curve in the Draw Test Harness

3.1 PCurve on Cylindrical Surface

The first example is a pcurve(line) on a cylindrical surface, this pcurve will produce a normal helix curve, ie. a spring, the Tcl script to test it in Draw Test Harness:

#
# make helix curve in OpenCASCADE.
# Shing Liu(eryar@163.com)
#2015-07-08 22:00
#

pload MODELING VISUALIZATION

cylinder aCylinder 6

line aLine2d 0 0 1 1
trim aSegment aLine2d 0 2*pi

mkedge aHelixEdge aSegment aCylinder 0 6*pi

vdisplay aHelixEdge

Save the above Tcl script to d:/tcl/helix.tcl, and load it in the Draw Test Harness, the result is:
And different slope of the pcurve(line) will cause different pitch of the helix:

• when the slope k = 1, the pcurve is

line aLine2d 0 0 1 1 

• when the slope k = 1.0/5.0, the pcurve is:

line aLine2d 0 0 5 1 

• when the slope k = 1.0/10.0, the pcurve is:

line aLine2d 0 0 10 1 

You can modify the pcurve slope to have a test. Finally you can sweep a circle along the helix curve to get a solid shape:

3.2 PCurve on Conical Surface

The same pcurve on conical surface will get the following result:

3.3 PCurve on Toroidal Surface

When the pcurve in on toroidal surface, you will get the the follow result: Different slope also can cause different pitch:

Also you can sweep a circle along the helix curve to get a solid shape:

Tcl script list below:

#
# make helix torus(Ring Type Spring) in OpenCASCADE.
# Shing Liu(eryar@163.com)
#2016-02-20 21:00
#

pload MODELING VISUALIZATION

# use torus surface.
torus aTorus 10 2

set aSlope 0.05
line aLine2d 0 0 $aSlope 1
trim aSegment aLine2d 0 2*pi

# make edge by the pcurve.
mkedge aHelixEdge aSegment aTorus 0 2*pi/$aSlope

# there is no curve 3d in the pcurve edge.
# so need this to approximate one.
mkedgecurve aHelixEdge 0.01

wire aHelixWire aHelixEdge

# make the profile.
circle aProfile 12 0 0 1 1 1 0.3
mkedge aProfile aProfile
wire aProfile aProfile
mkplane aProfile aProfile

# display the profile.
vdisplay aProfile aHelixEdge

# loft the circle along the helix curve.
pipe aSpring aHelixWire aProfile

# display the result.
vdisplay aSpring
#vsetmaterial aSpring steel
vsetgradientbg 180 200 255 180 180 180 2
vsetdispmode 1
vzbufftrihedron

set ray tracing
if { ! [catch {vrenderparams -raytrace -shadows -reflections -fsaa -rayDepth 5}] } {
  vtextureenv on 1
}

4.Conclusion

PCurve is a powerful modeling method, to make helix shapes in occQt to help you understand pcurve better, then you can also can model some intereting shape based on pcurve.

I will translate the above Tcl scripts to C++ in occQt soon.

5. References

• 5.1 OpenCASCADE Make Bottle Tutorial. 2016
• 5.2 OpenCASCADE BRep Format. 2016
• 5.3 OpenCASCADE Draw Test Harness User Guide. 2016
• 5.4 Helix definition: http://mathworld.wolfram.com/Helix.html
• 5.5 Make Helix Curve in OpenCASCADE, http://www.cppblog.com/eryar/archive/2015/07/09/211212.html
• 5.6 OpenCASCADE Ring Type Spring Modeling http://www.cppblog.com/eryar/archive/2016/03/05/212931.html

[eryar]

The helix have been added to occQt: https://github.com/eryar/occQt/wiki/Make-Helix-Shape-in-occQt