Creating and Fitting Curves

After you have fashioned your model from the foam cube, scan the model's surface to produce a series of scan lines that represent your creation. If the scan lines do not look exactly the same as the foam model, keep in mind that the model was handcrafted, and as a result, small surface degradations may have been created during the model's construction. It is also entirely possible that the scanning device made errors due to a discrepancy in stated construction tolerances. Regardless of the cause of the errors, it should be understood that the primary role of the scan lines is to provide a guide for the dynamics of the model. Before beginning the surface modeling, use the scan lines to garner information about the model.

Similar to sketching on the foam cube, the first step in the surface modeling process is to create a center line based on the scanned input.

To view all of the scan lines

Open the wire file Curve Fitting.wire.

Pick all of the scan lines.

Choose the View > Look at tool.

The scan lines used in the tutorial are degree 1 curves. When using the Pick > Component tool, the scan lines can only be selected as curves, not sections.

With all of the scan lines displayed, you might find that the model is cluttered. To make your work appear cleaner, isolate the scan line that represents the center line.

To isolate the center line

Click and hold the X-scans layer button to open the menu.

Turn off the Visible option.

Repeat Steps 1 and 2 for the Z-scans layer. In the end, only the Y-scan lines should remain visible.

Choose

Pick > Object and select the scan line that represents the center line.

Choose ObjectDisplay > Hide Unselected. All unselected scan lines are hidden - only the selected center scan line is visible. (To make the hidden lines visible again, choose ObjectDisplay > Visible from the menu).

Commit these steps to memory - later in the tutorial you will be asked to isolate a particular scan line or make a layer visible or invisible.

You may recall that when you were in the workshop you found it difficult to shape the center line in one step. To complete the model, you shaped three main surfaces (the front, middle, and rear) and completed the model by adding two blends. Following the workshop example, fit a curve to the top part of the center scan line. Use an automatic fitting algorithm, such as the Curve Edit > Fit curve tool, to undertake this part of the project.

To fit the top part of the center line using the Curves > Fit Curve tool

In the Viewing Panel, switch to the side view by selecting the middle arrow in the bottom row of arrows.

Double-click the Curves > Text

tool to produce the options box.

Select the scan line that represents the center line and set the options in the Fit Curve Control as shown in the image below.

The Curves > Text tool selects the entire scan line, but initially you will be interested in selecting only the top part of the curve.

Pick the cross that lies adjacent to the blue manipulator and move along the scan line until only the top portion of the curve is selected.

Your curve should resemble the above image. As you gain more experience with surface modeling, you will learn to judge the placement of the CVs. Later in the tutorial, the term "Hull / CV distribution" will be used to describe the placement of CVs.

By moving the crosses and changing the fitting method, you can influence the CV distribution.

Another method for achieving a good CV distribution is to pick the CVs and move them to the desired position. However, this method is not recommended at this point in the modeling process as moving CVs will destroy the construction history of the curve.

Repeat Steps 2 - 4 for the front and the rear portions of the center line.

After fitting the three parts of the center line, your curve should resemble the image below.

To view all of the CVs associated with an object, click the box of the CV/Hull option located in the Display section of the Control Panel, so a check mark appears.

Next, blends will need to be created between the three main curves. Another semi automatic tool, the Blend curve, will be utilized to perform this task. Blend curves can be intimidating to the beginner, so for this reason you will be asked to use a limited number of the simpler options.

Creating blends between the main curves

To create the blends using blend curves

Click and hold down the Y-scan layer button to open the menu.

Choose Set state > Reference from the layer menu.

Choose Curves > Blend curve toolbox

to open the toolbox.

Choose the BlendCrv Tools > Blend curve create

tool from the toolbox. (Click the BlendCrv Tools tab to see the menu or click the icon).

Place a blend point (the first point of the blend curve) on the endpoint of the top curve.

Place the second blend point on the endpoint of the back curve.

A straight line will appear between the top curve and the back curve.

Repeat Steps 4 to 6 for the other side of the curve.

The number of blend points can be unlimited, but it should be understood that each new blend point increases the number of spans on the blend curve. Also, a blend point holds a vast array of information that defines the shape of the blend curve. A blend point is essentially a guide, or a point of reference, for a blend curve that could interact with a curve, a surface, an isoperimetric curve, or a curve-on-surface. To access the information associated with the blend point, open the Information window.

To use the Information window

Choose the Pick > Point Types > Blend point

tool and select one blend point.

Choose the Windows > Information > Information window menu item.

The value for the Continuity option should be set to 0. Continuity is a measurement of how two surfaces or curves connect.

For the purposes of our model, the blend curve should appear as a bowed transition between the two scan lines. In order to change the blend curve, we will need to change the Continuity measurement to 2.

An explanation of Continuity types

POSITION (G0)

This type of continuity between curves implies that the endpoints of the curves have the same X,Y, and Z position in the world space. This is the minimum requirement for obtaining G0.

TANGENT (G1)

This type of continuity between curves implies that the tangent CVs must be on one line.

CURVATURE (G2)

This continuity type impacts the third CV of the curve. All three CVs have to be considered in order to maintain a smooth curvature comb.

If a curvature comb does not have a smooth transitional line, further continuity levels can be applied but are outside of the scope of this tutorial. In order to improve the curvature comb, manually modify the position of the three CVs that constitute the G2 continuity.

To change the constraint continuity of a blend point

Select one blend point.

Choose the BlendCrv Tools > Constraint Continuity > Blend constraint G2 tool.

The blend curve changes from a straight line to a smooth transitional curve between the two scanned lines. Note also that the value for Continuity has changed to a 2 (G2) in the Information Window. If the shape of the blend curve is not perfect, you will have an opportunity later in the tutorial to manipulate it.

Repeat Steps 1 & 2 for the remaining three blend points (adjusting continuity at each end of both blend curves).

To examine the proximity of the blend curve to the scan line

Choose

Pick > Nothing.

Zoom into the scene until you have a clear view of the blend curve and the scan line.

Select the blend curve.

Turn on the CVs (CV/Hull in the Control Panel).

The CV distribution of the blend curve is very good, but the blend curve does not fit to the scan line. How could you correct this problem?

Before you make a decision about how to correct this problem, you should stop to consider some aspects of the work you have completed.

The CV distribution of the blend curve is satisfactory - so, there's no need to change it. That leaves you with the endpoints - because the top and rear curves still have their construction history, you should use small incremental movements to manipulate the endpoints.

To reactivate a tool's option box using the Query Edit tool

Choose the Object edit > Query edit

tool.

Select the rear curve.

The Fit Curve Control window and the blue manipulators will appear again.

Move the upper cross down toward the end of the curve.

Because the blend curve is still attached to the curve (with G2), it will follow.

While you move the cross of the fitted rear curve, pay attention to how close the blend curve comes to the scan line.

At this point in the tutorial, you should be comfortable with using your eyes to judge the deviation to the scan line. Within the confines of this tutorial, your work does not have to be precise, but for situations where your work must be more professional, you will require the assistance of a measurement tool, such as a Locator.

To use a Locator tool in measuring a curve-to-curve distance

Click and hold the Y-scan layer button to open its menu and choose Set State > Pickable.

Choose the Locators > Deviation > MinMaxCrvCrv deviation tool.

Select the scan line and the curve(s) you want to measure. More than one curve can be selected.

The deviation between the selected items will be measured and appear as a locator.

In the Control Panel you can switch the deviation locator on or off by selecting/deselecting the Deviation checkbox (the curves need to be picked first).

Modify your curves and note how the deviation locator updates the deviation status.

After you are satisfied with the results, select and delete the deviation locator.

If you are still not content with the match between the scan line and the blend curve, you can explore another method for reshaping the blend curve.

Blend points are located at the ends of blend curves. Each blend point contains information that can be read in the Information window (Windows > Information > Information window).

For complete control over a shape, you should always turn on CVs in the Control Panel (Cv/Hull).

To use the blend curve edit manipulator in the Blend curve toolbox

Choose

Pick > Nothing.

Pick the upper blend point.

Open the blend curve toolbox.

Choose the BlendCrv Tools > Blend curve edit

tool.

A new manipulator will appear that features a blue sphere and a blue rectangle.

With the

, pick the sphere, hold down the mouse button, and move the mouse. Note the movement of the blend curve.

Repeat Step 5 using the rectangle.

When manipulating the rectangle, the second and third CVs move while manipulating the sphere will move just the third CV.

Up to this point in the tutorial, you have learned two methods for fitting a blend curve to a scan line. The first method changed the reference points. If the first method does not produce sufficient results, as a last resort, use the manipulator to change the shape of the blend curve.

Repeat the entire sequence for the front blend.

In a real job environment where time is often a critical factor, when changing the connection quality of the blend point to CURVATURE quality (G2) you should simultaneously select both blend points to save time.

You will recall that earlier in the tutorial you conducted a deviation control by hand and used your eyes to judge your work.

The next step is to use a curvature comb to check the smoothness of your curve connections.

To check the curvature of curves

In the Y-scan layer menu, choose Set state > Reference.

Select all of the curves.

Choose the Locators > Curve curvature

tool.

Locators will appear that show curvature combs connected to the selected curves. Curvature combs are locators, and as such, you can access information about them through the menu item Windows > Information > Information window.

In most cases though, the curvature comb locator will not provide you with all of the information you may require. To gain more information, select the Curvature shelf from the Control Panel and change the Comb Scale value.

To change the Comb Scale value

Select the Curvature button from the Control Panel to open the Curvature shelf.

Change the values for the Comb Scale and the Samples options.

Having changed the Comb Scale and Samples values, your curve should resemble the image below.

The comb shows a significant jump in values at the position of the blend curves (not a smooth transitional curvature comb). If you were to leave the curves in their current state, the end result would take into account the distortion of values as pointed out by the curvature combs. To remove any curvature distortions you should adjust the combs in a finite fashion. As the manipulation of the curves is a complex task, be careful to adjust the combs in small increments. In fact, it could take you a matter of years to perfect the art of manipulating curves. However, in the interests of time, there are some hints that should speed-up the process.

Factors to consider when manipulating curves

Watch the curvature plot of the top curve. It has a clean arc because the CVs are placed at regular intervals.

Try to increase the curvature at the end of the top curve. To accomplish this task, directly manipulate some of the CVs.

Moving the second CV always has a significant impact. Manipulate it very slowly in order to keep the close deviation to the scan line that you have already achieved.

To model CVs directly

Pick the top curve.

From the menu, choose Delete > Delete construction history.

You will be prompted to make sure that you want to delete the construction history for the curve. Click YES to confirm.

The top curve will no longer have a Fit Curve history.

Select the highlighted CV shown in the image below.

At the bottom of the Control Panel, select the Move CV tool.

In the CV Move shelf, set the two values associated with Mode to SLIDE and CV.

The selected CV will now appear with two arrows that point in the direction of the available movement associated with the CV. The direction will always point toward the next CV.

Pick one arrow and move the CV slightly.

Watch the curvature and how the curvature comb changes.

Remember, the objective of this exercise is to strike a balance between a smooth transitional curvature comb and a close fit to the scan lines. As you experiment with different strategies and methods for achieving the desired results, you may find that you will need to correct the endpoints of your first three curves.

Your finished curvature comb should resemble the image below. It may require a significant investment in time to achieve the same results but the experience you gain from the exercise will help you later in your surface modeling career.

To clean up your work

Choose the Delete > Delete all locators menu item. All of the green curvature combs should disappear.

Choose Layers > New to produce a new layer.

Double-click the new layer, then type "Center Line CRV" and press Enter.

With the new layer still selected, pick all of the new curves that represent the center line.

Click the new layer button, hold down the mouse button and move the mouse down to Assign. The selected geometry will be assigned to the new layer.

Using the same technique as Step 5, make the new layer's contents invisible by moving the mouse down to Visible in the new layer menu. The check mark beside the option will disappear and the geometry assigned to the layer will become invisible.

From the menu, choose ObjectDisplay > Visible to make all of the Y-sections appear.

Repeat Step 6 to make the layer Y-scan invisible.

Save your work.

Summary

Blend points have special information that can be accessed through the Windows > Information > Information window menu item, or can be changed via the options available in the Blend curve toolbox.

Curve fitting is an intricate process that should lead to striking a balance between a smooth transitional curvature comb and a close deviation to the scan line.

Curve positions are never fixed. Blend curves can change the endpoints of main curves.

Following the process detailed at the beginning of the tutorial, you can define the shape of the other two directions (the front surface, or X- scans, and the top surface, or Z-scans).

While fitting the new curves you will be introduced to some new methods. In general though, you will be able to use the same processes detailed in this section to complete the next step.

Fitting Curves to X-scans

Some characteristics of X-scans

X-scans run perpendicular to the center line, whereas Y-scans run parallel to the center line.

modeled X-scans are symmetrical, in that one half is the same as the other half.

Because of the X-scan characteristics, it is possible to model half the model and mirror the other half.

Mirroring saves time, but it can also produce a problem that must be addressed. Running along the Y-plane at the Y0 position, whole surfaces, such as the top surface, are seamless. On the other hand, when employing the "half-side-modeling" method, two surfaces and a connection seam are created. Connection seams lead to modeling problems with curvature combs.

For example, the image below shows a surface that covers the right half of the model. The left half of the model was mirrored from the right half. Note that the curvature combs have a seam crossing the center line. This seam can be modified, but special attention will have to be paid to the manipulation of the surface.

In contrast, the image below shows one surface covering the entire top of the model. The curvature combs crossing the center line are smooth, and as a result, you will never have to check the appearance of the curvature comb crossing the Y0 position.

To avoid the problems created by mirroring, all surfaces that cross the center line should be constructed as one surface.

This is not an absolute rule. There are other models and situations where it may be better to employ the mirroring strategy.

To fit a curve that crosses the center line

Make the scan lines from the X-scan layer visible and pickable. (Use the Visible and Set State > Pickable menu items for the X-scan layer).

Select one scan line from the middle portion and isolate it. (Use the ObjectDisplay > Hide Unselected menu item).

To fit a curve to a scan line, double-click the Curves > Text

tool to produce the option box.

Set the options as shown in those in the image below.

Use the Curves > Text tool in the same manner as detailed in "Establishing and creating the center line" section.

Once you have created the curve and matched it to the scan line, you can use it as a guide.

Choose

Pick > Nothing.

Select the new curve.

From the menu, double-click Edit > Duplicate > Mirror to produce the Mirror Options box.

Set the Mirror Across option to "XZ" and press Go.

Two points have now been produced, one at either side of the model, each with a corresponding position relative to the center line. The next step in the procedure will be to create the real curve.

Double-click the Curves > New curves > New Curve by Edit Points

icon to produce its option box.

Set the options as shown here.


Set this parameter...	To this value
Knot spacing	Uniform
Curve degree	2
Create guidelines	off

Create a straight curve between the two endpoints.

Use the Magnet tool (upper right corner of the display) to snap the new CVs exactly to the endpoints.

Choose Pick > Nothing

Delete the helper curves.

Select the middle CV and move the CV in the Z-direction to match the shape of the scan line.

As you manipulate the CV in the Z-direction, you may notice that you cannot model the shape of the scanned line with just one free CV. Eventually, you will need more CVs, but not before giving some thought to the maximum number of CVs you will require. To tackle this question, always start with the lowest degree (number of CVs) and increase the value in small steps. Employing a lowest-to-highest degree strategy should ensure that you do not overbuild your model.

To increase the number of CVs of a curve

Make sure that the curve is selected.

Turn on the CVs (Cv/Hull) in the Control Panel.

In the Degree text box located in the middle of the Control Panel, type in the value 4 and press Enter.

Click the Accept button in the lower right corner of the window.

With the increase in CVs there is also an increase in the freedom of movement. When moving CVs you should remember to always move corresponding CVs at the same time, otherwise, you will loose the symmetry of the curve.

Going forward with this exercise, you will encounter a problem when trying to change the position of the marked CV in the Y-direction. One solution to this problem is to select the CVs you intend to move on both sides of the center line and then center the pivot point. You will then be free to move the CVs using a non-proportional scale.

To move CVs using a non-proportional scale

Choose Pick > Nothing

Select the CVs highlighted in the image above.

Choose the Transform > Local > Center pivot

tool. Note that the green pivot point jumps closer to the center CV. The pivot point marks the balance point of the selected CVs. Your local source point for the next movement will be placed at the new location of the pivot point.

Choose the Transform > Non-p scale

tool and use the middle mouse button to move both CVs in the Y-direction, away from the Y0 position.

You will now be able to fit the curve to the scan line, but don't consume too much time measuring the deviations between the scan line and the curve. Instead, concentrate on trusting your eyes and developing an understanding of the CVs role.

After completing the top curve, continue creating the missing parts of the X-scan line. Use the same methods you learned when creating the center line (changing the endpoints of the curves, and modifying the blend curve using the manipulator).

Remember to check the curvature comb of your X-curves by selecting all the curves and then using the Locators > Curve curvature

Also, take care when polishing the curvature plot that you limit your movement to the non-proportional scale of the CVs on the top curve. To avoid destroying the symmetry of the curve, you should not use the SLIDE command if the curve runs across the Y0 position.

To save your work

Select all of your new curves and save them to a new layer named "X CRV".

Make sure that all the X-scans are visible again.

Make the X CRV layer and the X-scan layer invisible.

Save your work.

Summary

In this section you were introduced to the curvature plot and its relationship to half-modeling techniques.

As well, you were taught how to avoid a curvature peak in the plot that crosses the center line by building curves and surfaces across the middle.

But perhaps most importantly, you were instructed to always move CVs in groups of corresponding pairs to avoid losing the symmetry of the curve. The best practice for moving multiple CVs is to select the CVs as a pair, center the pivot point, and use the non-proportional scale for horizontal movements.

Fitting Curves to Z-scans

, will be used to fit a scan line from the Z-scan layer. The option box of the Object Edit > Align > Align tool is quite complicated, but most of the options pertain to matching surfaces. As you are concerned with curves, you will only need to interact with a few of the options.

To create a set of curves using edit point curves

Set the Z-scans layer to Visible and Set state > Pickable.

Isolate one scan line that encompasses the model.

Hide the unselected scan lines. (Use the ObjectDisplay > Hide Unselected menu item).

Create a degree 2 edit point curve at the middle portion of the scan line by snapping the endpoints to the scan line. (Use the Curves > New curves > New Curve by Edit Points tool).

Pick the middle CVs and move the CVs in the Y-direction until you fit the shape of the scan line.

With flat shapes, you may find it difficult to judge the shape of your curve. To get a better view of your work, go to the Viewing Panel by pressing Shift

. Inside the Viewing Panel, examine the four icons in the bottom rectangle. Make sure that the box beside the Perspective option does not contain a check mark. Inside the bottom rectangle, choose the square icon. You will now be able to dolly your view in a non-proportional manner that should provide for a better view of how your curve fits to the scan line.

To use the icons in the Viewing Panel

Press

and hold down the buttons.

Make sure that the Perspective option does not contain a check mark.

Choose the square icon. The icon will turn white to show that it is engaged.

Keep holding down the Shift

keys. (The Viewing Panel must remain open to execute the view change).

Use the mouse buttons to scale the view.

The right mouse button scales the view both horizontally and vertically, the middle mouse button operates on the horizontal scale, and the left mouse button is reserved for the vertical scale.

To return to the original view, choose the Perspective option and then remove the check mark. The view should return to the natural scale in the orthographic view.

If the non-proportional view is not sufficient, choose the circled arrow icon at the bottom of the Viewing Panel to spin the view. To return to the original view, use the black arrows that surround the car icons in the middle of the Viewing Panel.

To fashion the front/rear curve, use the same technique employed on the X-scans.

Tips for creating a set of curves using edit point curves

Use the Curves > Text

tool.

Mirror the fitted curves.

Create two degree 5 edit point curves.

Shape the degree 5 curves to fit the scan line. Remember to move corresponding CVs to maintain the curve's symmetry. As well, when moving CVs in the Y-direction, use the non-proportional scale and center the pivot.

When creating the transition between the front portion of the curve and the middle portion of the curve, use a degree 5 edit point curve to bridge the endpoints.

After completing work on the Z-scan line, the degree 5 edit point curve looks similar to the curve used in blending the center line. Note that the current straight line is not a blend curve. Instead, it is a degree 5 edit point curve that allows for the use of the Object Edit > Align > Align

To use the Align tool for aligning two curves

Choose the Z-scan layer option Set state > Reference.

Double-click the Object Edit > Align > Align tool icon to produce the option box.

Select the edit point curve at the marked point (blue arrow) to align the curve beginning with the selected end.

Select the top reference curve at the marked point (red arrow) to align the first picked curve to the second picked reference.

Set the Object Edit > Align > Align tool options as shown above.

By setting the Continuity option to TANGENT, you will notice that just the first and the second CVs are highlighted in yellow. If you change the Continuity to CURVATURE you will notice that the third CV is highlighted as well.

Repeat Steps 3-5 for the other side.

The Continuity level determines how many CVs are highlighted, or influenced. This knowledge is crucial to understanding the alignment of surfaces later in the tutorial.

The basic concepts behind the primary Continuity settings

POSITION means the first CV will be moved to the reference.

TANGENT means the first and the second CVs have to be moved to achieve the quality.

CURVATURE means that, in addition to the first and second CVs, the third CV will also have to be moved to achieve the quality.

Now, it should be clear that in order to achieve curvature continuity on both sides of the curve, a minimum number of 6 CVs is required. Use a degree 5 single span edit point curve to achieve these results.

To direct model a curve

To fit the curve to the scan line you can now use the SLIDE option in the CV Move shelf located at the bottom of the Control Panel. After sliding a CV, the Object Edit > Align > Align tool will always bring the CV back into alignment. By proceeding in controlled steps, you will achieve a proper deviation.

Also, don't forget the possibility of changing the start points of the reference curves. Click the first CV of the reference curve and move the CV while pressing Ctrl

(curve snap) along the scan line.

Three additional curves will have to be fitted to the Z-scan lines. The new curves will serve as guides for developing the front end surface and the transition surface. Use the methods previously described in this section to fit the Z-scan lines.

Your completed curves should resemble the image below - the spheres mark the endpoints of the curves.