Disclosure:

I did not participate in the Solid Edge ST6 beta this year, but I did mention on last year debriefing that surface and synchronous are like ice cream and chocolate so i hope for the best in June, all you read here is no guaranty it will show in the next release, simply because most of this is already in the software as of today .........

Lots of talk about conic curve and tangent. And since Solid Edge ST6 is on it way with new surface tools, why not take few minutes to better understand the theory behind all this.

To begin first, we will look at what are the different type of conic section and what are the different types of tangent condition available in Solid Edge.

The buzz around conic section, make me realize, people want conic section because they are easier to manipulate since they are produce from a formula, there is no guess in creating them. Unlike generic spline (nurbs) where you need to put more time to fully constraint them.

In Short people prefer to put back to back multiple segment of conic section rather than create a single spline. We could compare this to, we prefer to have a rectangle/polygon command then having to draw four lines

There is four kinds of

Conic sections are

This type of conic section is create when a plane is place perpendicular to a cone axis an we extract the curve at the intersection of the plane and the curve

This type of conic section can be create when a plane intersect a cone and the curve form a closed shape

This type of conic section can be create when a plane is parallel to the the side of the cone and the intersecting curve is open.

This type of conic section can be create when a plane intersect a cone at a specific angle

«…Which conic section is formed depends on the angle the plane makes with the axis of the cone, compared with the angle a straight line on the surface of the cone makes with the axis of the cone. If the angle between the plane and the axis is less than the angle between the line on the cone and the axis, or if the plane is parallel to the axis, then the plane intersects both halves of the double cone and the conic is a hyperbola….»

Let take few minute to look a a video to see those conic section.

OK know that we have a good understanding what are the different conic section let’s look a the different tangent condition

Before going there let review a tool call curve comb. This tool allow you to analyze the curvature of a system.

You can find this tool under the Inspect tab.

Two settings are available,

How to read the curve comb. The more curvature you have the higher is the spoke. A line will have no curvature thus no curve comb. can be display

Ok we can now look at different type of tangent condition offer by Solid Edge.

Based on which system you work a letter will be associate to a number. The letter itself for the purpose of this article is not important what I want to focus is the number. The bigger is the number the more variable are apply to the tangent

0 (connect)

The first tangent condition, is no tangent this mean two curve are touching and create a sharp corner.

1 (tangent)

This is a tangent condition where the curvature blend at the contact point.

By blend I mean the curvature of both curve are parallel at the contact point, you can see this when you activate the curve comb.

The spoke of the curve comb. Represent the intensity of the curvature and its direction. In the picture above, I apply a visual trick to show a tiny curve comb. on the straight line because a straigh line has no curvature.

If you want to test this yourself, zoom in at the contact point and draw a line on top of the first spoke of the curve comb. You will see it will be perpendicular to the line at the contact point.

Here two curve being tangen and we can see at the contact point the spoke being parallel. We can also see the curvature intensity of the red curve being higher than the blue one.

2 (Tangent & Equal curvature)

Here the curvature rate is equal at the contact point.

This can be display by the curve comb. Where we see the spoke having the same length at the contact point.

3 (Parallel tangent vectors)

Ok this one is little bit tricky, I will let Solid Edge explain by itself

«…When you use the Parallel Tangent Vectors Option, you ensure that the tangent vectors of the input curves are parallel. Because you can apply a tangent relationship between elements on different reference planes, the Parallel Tangent Vectors option is useful when all the curves that form a freeform surface must blend smoothly at their endpoints, which helps to ensure a smooth blend with an adjacent surface.

For example, when defining the curves for a lofted surface (G), curves (A) and (B ) were constrained using the Parallel Tangent Vectors option, then curves (B ) and (c) were constrained using the same option. Although the radius of curvature for each curve at its endpoint is different, the relative angles represented by the first and second edit points on each curve (D) and (E) are the same, due to the Parallel Tangent Vectors option…..»

4 (Parallel tangent vector + Equal curvature)

«… The Parallel Tangent Vectors + Equal Curvature Option combines the capabilities of the Parallel Tangent Vectors option and the Equal Curvature option. The constrained elements will be tangent, have equal curvature, and their tangent vectors will be parallel. The first element you select must be a b-spline curve….»

At the point of contact the spoke of the curve comb are equal, and we clearly see the first section of the control polygon being parallel (or collinear)

Below is an extrem, case showing the parallel state

The next step will be to make sure the first two segment of the control polygone are equal to keep the curvature under more control on both side on the contact point.

In the above picture dimensions are being used to establish a formula.

If you want to explorer a little bit more about curve and conic curve inside Solid Edge, on the left I have create a hyperbole, I have copy on the side and lock its shape.

Next I create a spline to match the Hyperbole. Looking at the curve comb., we see the curvature rate of the hyperbole being different, but the distribution is quite identical.

And I can control the shape up to 7 decimal point

So unless you want that kitchen mixer fly to mach 12………..

I do not pretend being the master guru of spline, conic section freestyle stuff or anything you can imagine after you smoke a joint.

But until we see what ST6 will do to enhance exiting functionality, I’m sure existing Solid Edge surfacing tools, can make your project look cool.

Do you have any cool surface design to share? Post picture in the comment area or sign-in and add them to the gallery section, be proud of your design.

I did not participate in the Solid Edge ST6 beta this year, but I did mention on last year debriefing that surface and synchronous are like ice cream and chocolate so i hope for the best in June, all you read here is no guaranty it will show in the next release, simply because most of this is already in the software as of today .........

Lots of talk about conic curve and tangent. And since Solid Edge ST6 is on it way with new surface tools, why not take few minutes to better understand the theory behind all this.

To begin first, we will look at what are the different type of conic section and what are the different types of tangent condition available in Solid Edge.

The buzz around conic section, make me realize, people want conic section because they are easier to manipulate since they are produce from a formula, there is no guess in creating them. Unlike generic spline (nurbs) where you need to put more time to fully constraint them.

In Short people prefer to put back to back multiple segment of conic section rather than create a single spline. We could compare this to, we prefer to have a rectangle/polygon command then having to draw four lines

**Conic section types**There is four kinds of

**conic section**, formed by the intersection of a plane and a cone.Conic sections are

**circle,****ellipse,****parabola**and**hyperbola**.*Circle*This type of conic section is create when a plane is place perpendicular to a cone axis an we extract the curve at the intersection of the plane and the curve

*Ellipse*This type of conic section can be create when a plane intersect a cone and the curve form a closed shape

*Parabole*This type of conic section can be create when a plane is parallel to the the side of the cone and the intersecting curve is open.

*Hyperbole*This type of conic section can be create when a plane intersect a cone at a specific angle

«…Which conic section is formed depends on the angle the plane makes with the axis of the cone, compared with the angle a straight line on the surface of the cone makes with the axis of the cone. If the angle between the plane and the axis is less than the angle between the line on the cone and the axis, or if the plane is parallel to the axis, then the plane intersects both halves of the double cone and the conic is a hyperbola….»

Let take few minute to look a a video to see those conic section.

OK know that we have a good understanding what are the different conic section let’s look a the different tangent condition

**Tangent**Before going there let review a tool call curve comb. This tool allow you to analyze the curvature of a system.

You can find this tool under the Inspect tab.

Two settings are available,

- Density of the spoke
- Magnitude (amplification) of the spoke

How to read the curve comb. The more curvature you have the higher is the spoke. A line will have no curvature thus no curve comb. can be display

Ok we can now look at different type of tangent condition offer by Solid Edge.

Based on which system you work a letter will be associate to a number. The letter itself for the purpose of this article is not important what I want to focus is the number. The bigger is the number the more variable are apply to the tangent

0 (connect)

The first tangent condition, is no tangent this mean two curve are touching and create a sharp corner.

1 (tangent)

This is a tangent condition where the curvature blend at the contact point.

By blend I mean the curvature of both curve are parallel at the contact point, you can see this when you activate the curve comb.

The spoke of the curve comb. Represent the intensity of the curvature and its direction. In the picture above, I apply a visual trick to show a tiny curve comb. on the straight line because a straigh line has no curvature.

If you want to test this yourself, zoom in at the contact point and draw a line on top of the first spoke of the curve comb. You will see it will be perpendicular to the line at the contact point.

Here two curve being tangen and we can see at the contact point the spoke being parallel. We can also see the curvature intensity of the red curve being higher than the blue one.

2 (Tangent & Equal curvature)

Here the curvature rate is equal at the contact point.

This can be display by the curve comb. Where we see the spoke having the same length at the contact point.

3 (Parallel tangent vectors)

Ok this one is little bit tricky, I will let Solid Edge explain by itself

«…When you use the Parallel Tangent Vectors Option, you ensure that the tangent vectors of the input curves are parallel. Because you can apply a tangent relationship between elements on different reference planes, the Parallel Tangent Vectors option is useful when all the curves that form a freeform surface must blend smoothly at their endpoints, which helps to ensure a smooth blend with an adjacent surface.

For example, when defining the curves for a lofted surface (G), curves (A) and (B ) were constrained using the Parallel Tangent Vectors option, then curves (B ) and (c) were constrained using the same option. Although the radius of curvature for each curve at its endpoint is different, the relative angles represented by the first and second edit points on each curve (D) and (E) are the same, due to the Parallel Tangent Vectors option…..»

4 (Parallel tangent vector + Equal curvature)

«… The Parallel Tangent Vectors + Equal Curvature Option combines the capabilities of the Parallel Tangent Vectors option and the Equal Curvature option. The constrained elements will be tangent, have equal curvature, and their tangent vectors will be parallel. The first element you select must be a b-spline curve….»

At the point of contact the spoke of the curve comb are equal, and we clearly see the first section of the control polygon being parallel (or collinear)

Below is an extrem, case showing the parallel state

The next step will be to make sure the first two segment of the control polygone are equal to keep the curvature under more control on both side on the contact point.

In the above picture dimensions are being used to establish a formula.

If you want to explorer a little bit more about curve and conic curve inside Solid Edge, on the left I have create a hyperbole, I have copy on the side and lock its shape.

Next I create a spline to match the Hyperbole. Looking at the curve comb., we see the curvature rate of the hyperbole being different, but the distribution is quite identical.

And I can control the shape up to 7 decimal point

So unless you want that kitchen mixer fly to mach 12………..

I do not pretend being the master guru of spline, conic section freestyle stuff or anything you can imagine after you smoke a joint.

But until we see what ST6 will do to enhance exiting functionality, I’m sure existing Solid Edge surfacing tools, can make your project look cool.

Do you have any cool surface design to share? Post picture in the comment area or sign-in and add them to the gallery section, be proud of your design.

Want more take time to look a those video

Thank you to Adam O’Hern who has great insight,

Conic