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3-D Spiral or Helix - Macromedia Freehand

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  1. Moderated Post

    Default 3-D Spiral or Helix

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    Mark Szlazak Guest
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  2. Moderated Post

    Default Re: 3-D Spiral or Helix

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    Mark Szlazak Guest
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    Default Re: 3-D Spiral or Helix

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    Judy Arndt Guest
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    Default Re: 3-D Spiral or Helix

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    James E. Talmage Guest
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    Default Re: 3-D Spiral or Helix

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    Mark Szlazak Guest
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  6. #6

    Default Re: 3-D Spiral or Helix

    James E. Talmage wrote:
    > A pencil and piece of paper is a 2D drawing platform, but that doesn't mean
    > you can't correctly construct drawings of 3D things on it. ;-)
    Okay James, you have put me to shame! :-)

    Because Mark Szlazak's page was titled 'Kinematics' I assumed he wanted to
    describe a helical motion path. I was thinking that software like
    'Mathematica' (expensive) would be able to plug in the formula and spit out
    the visuals.

    I've been playing around with the Extrude tool and have come up with an idea
    for a 3-D spiral. Maybe, Mark, you could adapt this to your needs.

    [url]http://www.judyarndt.ca/fhmx/helix_extrude.gif[/url]

    Judy Arndt
    --
    FHMX 11.0.2 (Build 92)
    Mac G4, OS 10.3.3

    Judy Arndt Guest

  7. #7

    Default Re: 3-D Spiral or Helix

    Hello Judy and thank you for the tip. Your correct about the helix being a
    kinematic path for one point. I would like a spiral path like the one you have
    demonstrated but without a changing radius from it's axis and of only point
    thickness to it's line.

    mszlazak Guest

  8. #8

    Default Re: 3-D Spiral or Helix

    Well, this is pretty quick and dirty but it will give you a 'skeleton' of
    your helix which you can rotate to suit your needs. No matter how you build
    with the 3-D Extrude feature, you are still left with an extrusion built of
    a zillion polygons, not a single dashed stroke.

    [url]http://www.judyarndt.ca/fhmx/extrude_helix_constant.gif[/url]

    I think you need Mathematica -- only $1,880 for a commercial license. :-)
    [url]http://www.wolfram.com/products/mathematica/index.html[/url]

    Judy Arndt


    mszlazak wrote:
    > Hello Judy and thank you for the tip. Your correct about the helix being a
    > kinematic path for one point. I would like a spiral path like the one you have
    > demonstrated but without a changing radius from it's axis and of only point
    > thickness to it's line.
    Judy Arndt Guest

  9. Moderated Post

    Default Re: 3-D Spiral or Helix

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    mszlazak Guest
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  10. #10

    Default Re: 3-D Spiral or Helix

    James, I gave the wrong spec for the "oblique" view translation along the S-axis. It's not 75 units but 235 units. I hope that this didn't caused confusion with figure 13.
    mszlazak Guest

  11. #11

    Default Re: 3-D Spiral or Helix

    "No matter how you build with the 3-D Extrude feature, you are still left with
    an extrusion built of a zillion polygons, not a single dashed stroke."

    Not if you do it the way I suggested in my first post on this thread. That is,
    if you:

    1) Draw a horizontal line, black stroke, no fill.
    2) Apply the Extrude Tool to it, extruding it into a "flat plane."
    3) Set the twist parameter for as many turns as you want.

    After releasing the Extrusion, ungrouping, etc., you will end up with a double
    helix with its two coils connected at the ends. Delete the two segments which
    connect the ends and you have the two spirals. Each one is a single, open,
    unfilled path (which Mark could then give any dash attribute he desires).

    Trouble is, this generates a vanishing-point perspective, not a parallel
    perspective, which the other drawings in the doent appear to be, and which
    Mark seems to be meaning by "oblique". FH's Extrude does not do parallel
    perspective.

    "James, I gave the wrong spec for the "oblique" view translation along the
    S-axis. It's not 75 units but 235 units."

    Mark, you do understand, don't you, that without a value for the radius, the
    axial translation (the "rise" of the spiral) doesn't describe the spiral? That
    is, the 80 degrees of your coil's rotation can traverse a height of 75, 235, or
    any other value and all you are doing is changing the scale of the height.
    Without a radius, you have no idea of the *proportion*. That is, with only the
    axial distance, the coil could be as tightly wound as a Slinky (large radius),
    with its coils almost touching; or it could could be stretched out like a shock
    absorber spring (small radius)--or anything in between--and still meet your
    criteria of such-and-such distance for 80 degrees of sweep.

    Now, as an aside, it sometimes seems as perhaps you are just asking how to
    manually trace a smooth curve along the points of the existing Figure 13. That
    would be a simple matter bringing the image into FH, putting it on a background
    layer, and using the Pen tool to place about 3 or four curve points per coil
    and adjusting their handles. But I'm assuming you want a method for building a
    reasonably mechanically correct parallel perspective of a coil, which is
    "tilted" to some degree from the line of sight (not just a side view).

    Constructing such a view is actually fairly easy. You can draw a full set of
    such springs (at various angles of tilt) in about 10 minutes. Because this fits
    in with a little project of mine, I'm assembling a PDF which will demonstrate.
    But I'm going to be gone all weekend at a BMW (motorcycle) camp/cookout/ride
    rally, so I may not have time to finish it before Monday. But the basic steps
    are:

    1) Draw a circle of the radius of your coil. Think of this as the "top view"
    of the spring. Split the circle at its top and bottom points to have two
    semi-circles. (It helps conceptually to color the two halves differently.)

    2) Clone the above (you'll need it later) and use the clone to build a "side
    view" of the coil, as follows: Begin by moving the right semicircle straight
    down so that its top snaps to the bottom of the left one. You now have an "S"
    curve. Group the two halves of the S. Scale the group vertically to the height
    of the rise of 360 degrees of sweep ( this would be 4.5 X your value for 80
    degrees of sweep). This "squashed" S is beginning to resemble the side view of
    a coil, but you are not there yet.

    3) Determine the slope of the coil. This is easily done mathematically: The
    continuous slope at any point along the coil is the slope of the diagonal of a
    rectangle which has a height of the coil's axial rise and a width of its
    cirference. (Think of rolling out and flattening the wall of a cylinder
    which contains the coil.)

    4) In the path of the "squashed S", select just the center point and rotate it
    about its own center the amount of the slope. Do the same for the top point and
    bottom point.

    5) The points which are at the apexes of the two curves are on a plane
    perpendicular to to the rotation just performed. Their handles need to "sloped"
    toward/away from you. To add "slope" to these two points, you would simply
    scale each about its own centers by the sine of slope angle. (Same principle as
    foreshortening an ellipse which represents a circle which lies on a tilted
    plane.)

    6) Now you have the original circular top view, which can be thought of as
    looking down the thrust line of the spring, or in other words, as a view of the
    spring rotated 0 degrees. And you have a side view which can be thought of as
    looking at the spring rotated 90 degrees. Put these two views side by side and
    take a careful look, imagining the top view rotating into the side view. Make a
    mental note of which half of the top view would rotate toward you and which
    half would rotate away from you. Then select coresponding endpoints of
    corresponding halves and perform a Blend between them. Do this for each half.
    If you use 8 intermediate steps in both blends, they will align to each other
    correctly and you will have a coil shape for each 10 degrees of tilt. Ungroup
    the Blends, and just step-and-repeat the coil of the desired tilt for a spring
    of any length.

    Like I say, easier shown than verbalized. More to come later.

    JET

    JET@BB Guest

  12. #12

    Default Re: 3-D Spiral or Helix

    Hi JET,

    Sorry about not giving radius or diameter measures for each of the three
    points A,B,O.
    I just wanted the construction steps in general for any radius.

    Anyway, I appreciate your spending the time to go into all this, and look
    forward to your examples after the weekend.

    Mark



    mszlazak Guest

  13. #13

    Default Re: 3-D Spiral or Helix

    What JET is describing as a spring construction is similar to this tutorial
    written by Ian Kelleigh:

    [url]http://www.freehandsource.com/_frames/_tips/_archive/tip_week068.html[/url]

    Instead of building the blend from ellipses filled with a gradient, you
    could use a smaller ellipses, basic black fill, and fewer blend steps. This
    would give you the appearance of a dotted line on each loop of the spring.

    Judy Arndt

    mszlazak wrote:
    > Sorry about not giving radius or diameter measures for each of the three
    > points A,B,O. I just wanted the construction steps in general for any radius.
    Judy Arndt Guest

  14. #14

    Default Re: 3-D Spiral or Helix


    What are your twist settings? Following your instructions below, if I set
    Static Twist to 3600, (ten 360 rotations) I get a very rough spiral. Paste
    in a horizontal line with many points added as profile, and the spiral
    smoothes out, but is made of pie-shaped wedges.

    Judy Arndt

    JETBB wrote:
    > "No matter how you build with the 3-D Extrude feature, you are still left with
    > an extrusion built of a zillion polygons, not a single dashed stroke."
    >
    > Not if you do it the way I suggested in my first post on this thread. That is,
    > if you:
    >
    > 1) Draw a horizontal line, black stroke, no fill.
    > 2) Apply the Extrude Tool to it, extruding it into a "flat plane."
    > 3) Set the twist parameter for as many turns as you want.
    >
    > After releasing the Extrusion, ungrouping, etc., you will end up with a double
    > helix with its two coils connected at the ends. Delete the two segments which
    > connect the ends and you have the two spirals. Each one is a single, open,
    > unfilled path (which Mark could then give any dash attribute he desires).
    Judy Arndt Guest

  15. #15

    Default Re: 3-D Spiral or Helix

    JET and Judy,

    Is it possible to combine your approaches to the extrusion method. I quickly
    tried a JET type approach by creating a square, removing its lateral sides,
    shrinking the remaining top and bottom lines to a pixel length each, then
    extruding this with a spiral twist which gives a double helix. As JET points
    out, the extrusion isn't parallel but Judy used a custom profile in a previous
    spiral example, I was wondering if a profile could be used to compensate for
    the non-parallel extrusion to give a parallel one.

    mszlazak Guest

  16. #16

    Default Re: 3-D Spiral or Helix

    A profile (think of the shape on an inclined plane) would compensate for the
    diameter change, but the extrude tool would gradually reduce the spacing of
    the coils as you get her away.

    Here's a method using a single extrude twist followed by Transform Effect.

    1. Draw horizontal line. Use Add Points Xtra once to add a point to the
    center of the horizontal line.
    2. Extrude with 360 degree twist.
    3. Release extrude and ungroup.
    4. Delete everything but a single 360 degree coil.
    5. Find the x and y distances between coil endpoints by snapping a
    rectangle's corners to the points. Note distances.
    6. Select coil and apply Transform Effect with Copies and Move, using noted
    x and y distances.
    7. Separate attributes.
    8. Select all coils. Join.
    9. Apply dashed stroke.

    Judy Arndt

    mszlazak wrote:
    > JET and Judy,
    >
    > Is it possible to combine your approaches to the extrusion method. I quickly
    > tried a JET type approach by creating a square, removing its lateral sides,
    > shrinking the remaining top and bottom lines to a pixel length each, then
    > extruding this with a spiral twist which gives a double helix. As JET points
    > out, the extrusion isn't parallel but Judy used a custom profile in a previous
    > spiral example, I was wondering if a profile could be used to compensate for
    > the non-parallel extrusion to give a parallel one.
    >
    Judy Arndt Guest

  17. #17

    Default Re: 3-D Spiral or Helix

    Hi Judy. You technique works well. I can see how it lessens problems with the
    "non-parallel" extrude.

    I'm still waiting on JET's S-curve technique. I tried following his
    instructions but don't get anything close to a spiral.

    Mark.

    mszlazak Guest

  18. #18

    Default Re: 3-D Spiral or Helix

    (Bike trip got rained out. Bummer.)

    [url]http://www.IllustrationETC.com/FHBuds/FHCoils.pdf[/url]

    3 page PDF. About 75k.

    "What JET is describing as a spring construction is similar to this
    tutorial."

    They are both about coils, but beyond that they really have different
    subjects. That tutorial is all about using a blend-on-path to "flesh out"
    the thickness of the "wire" on a coil, give it shading, and achieve the
    overlapping of the coils. What I am describing is an attempt to mechanically
    derive a view of the centerline of a coil with some measure of accuracy,
    based upon ordinary orthographic projection. In other words, I am describing
    a way to more properly draw the first step of that tutorial, rather than
    just eyeballing a "loopy path that looks like a spring."

    I am then using a Blend between two views which seem to me
    mechanically-justifiable, not for shading, but in order to eliminate the
    tedium of having to similarly construct from scratch views of coil which are
    tilted at various angles relative to the line of sight. I'm not doing
    anything at all to "flesh out" the wire of the spring, which is what all but
    step 1 of that tutorial is all about. In this case, all we are seeking is a
    more accurate centerline.

    "What are your twist settings? Following your instructions below, if I set
    Static Twist to 3600, (ten 360s rotations) I get a very rough spiral."

    I arbitrarily used 720 degrees, which here results in an acceptably smooth
    curve. There are no polygons or wedges. But I see what you mean when you
    increase the number of revolutions. Here, noticable faceting seems to start
    around 900. I figure one should be able to push it a little bit more by
    using the retract and auto-extend buttons to smooth the curves a bit.

    However, I do not seem to be allowed to enter 3600. The highest value the
    field will accept is 1800. Is there some other value which balances with the
    Twist setting and which is letting you enter a higher value? Maybe a
    difference on platforms (I'm on Windows.)?

    JET



    James E. Talmage Guest

  19. #19

    Default Re: 3-D Spiral or Helix

    James E. Talmage wrote:
    > [url]http://www.IllustrationETC.com/FHBuds/FHCoils.pdf[/url]
    > I am then using a Blend between two views which seem to me
    > mechanically-justifiable, not for shading, but in order to eliminate the
    > tedium of having to similarly construct from scratch views of coil which are
    > tilted at various angles relative to the line of sight.
    That's a very elegant solution and should be ideal for constructing the
    motion path that Mark needs.
    > However, I do not seem to be allowed to enter 3600. The highest value the
    > field will accept is 1800. Is there some other value which balances with the
    > Twist setting and which is letting you enter a higher value? Maybe a
    > difference on platforms (I'm on Windows.)?
    The slider only goes to 1800. I'm able to enter higher values in the
    numerical field. For a Static profile I was adding points to a horizontal
    line and pasting that in. This smooths the extrusion but builds polygons.

    I was able to do an 'almost orthographic' extrusion by working on a page in
    the lower left corner of the pasteboard and extending the vanishing point to
    the upper right corner of the pasteboard (x:14400 y:14400).

    Judy Arndt
    --
    FHMX 11.0.2 (Build 92)
    Mac G4, OS 10.3.3


    Judy Arndt Guest

  20. #20

    Default Re: 3-D Spiral or Helix

    "The slider only goes to 1800. I'm able to enter higher values in the
    numerical field."

    Mine will let me enter higher values, but as soon as I leave the field, it
    reverts to 1800.

    "For a Static profile I was adding points to a horizontal
    line and pasting that in. This smooths the extrusion but builds polygons."

    For kicks, I tried enveloping the Extrude results to remove the convergence,
    and also tried pasting into AI to use the "perspective" feature of the Free
    Transform tool; but neither gave very good results.

    I would have liked for both FH's Extrude and its Perspective Grid to have
    been given an optional parallel mode.

    JET


    James E. Talmage Guest

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