1. Smooth Sketching
Understanding splines in the
SOLIDWORKS sketcher

2. Smooth Sketching Agenda Crash Course in Continuity Conics Spline
Style Spline
Style Spline solve states
Spline vs. Style Spline
Using both splines together
Questions

3. Understanding Continuity
What is it?
Smoothing
As geometry transitions from one “type” to another, the transition is smooth
Splines: How smooth the curve is throughout its length (internal continuity)

4. Understanding Continuity
Why is it important?
What are you designing? What are the requirements?
Material Finish very smooth?
Will the product be held? How should it feel?
Are there lots of smooth transitions between topology?

5. Understanding Continuity
How is it defined?
To a CAD user, this consists of three factors
Direction vector
Radius of curvature
Vector magnitude, weight

6. Understanding Continuity
How is it defined?
Parametric Continuity:
C-1: Discontinuous geometry
C0: Contact, Position etc.
C1: First derivative continuity, Tangency
C2: Second derivative continuity, Curvature Continuous
C3 3rd derivative continuous – C3 continuous, rate of change of rate of change

7. Understanding Continuity
How is it defined?
Geometric Continuity:
G0 and G1 continuity are basically the same as C0 and C1
G2: “Equal Curvature”
The radius of curvature is the same
Magnitude may be different
It can be less precise, but gives the user more control
SOLIDWORKS sketch curves use G2 continuity

8. Understanding Continuity
How does it work in SOLIDWORKS?
Constraints, this makes it parametric
Sketch Relations – Coincident, Tangent, Equal Curvature
Managed by the sketch solver
Modeling constraints – Boundary, Surface Fill, Loft etc.
Managed by our geometry kernel

9. Understanding Continuity
Checks and Balances
Variety of tools to check curvature
Curvature combs (Sketch and Surface)
Zebra stripes
Curvature analysis
Tangent Edge Phantom font
Applying a shiny appearance to a model

10. Conics Ellipse, Parabola, Hyperbola (..and yes circle too)
What are they?
Intersection of a plane and a cone
The angle determines curve type
Hyperbola
Ellipse
Parabola

11. Conics Rho Factor B = A/B A 0 < rho < 0.5 = Ellipse
rho = 0.5 = Parabola
0.5 < rho < 1 = Hyperbola

12. Conics Ellipse, Parabola, Hyperbola Why are they useful to a CAD user?
Math is simple
2nd order curve: not prone to inflections
Can accommodate a wide variety of shapes
Make excellent bridge curves
Easily constrained to adjacent geometry

13. Conics Ellipse, Parabola, Hyperbola What are the limitations?
Not supported in 3D
G2 continuity
YES this can be done
Right now they can be G2 to curves that are degree 3 and higher (splines)
Making a conic G2 to something removes its degrees of freedom drastically

14. Splines Spline, Style Spline
They are both curves, but very different curves
They are both used to create continuous, freeform shapes
They use known mathematical equations, not something we “made up”

15. Introduction and Background
QUICK HISTORY LESSON!
Introduction and Background
We have two spline types in SOLIDWORKS
Late 1800’s
Mathematicians:
Sergei Bernstein
Nikolai Lobachesvsky
1950’s
1960’s
1940’s
1970’s
NURBS
Curves in
CAD systems
1980’s
STYLE SPLINE
Bézier Curve
SPLINE or
STYLE SPLINE
B-Spline

16. Spline It’s a B-spline of third degree (cubic)
It uses through points and handles for shaping
It can be shaped very quickly
More control you ask of it, the harder it is to manage
Tip: Keep it simple!

17. Style Spline
It can be a Bezier curve or a B-spline (more on that later)
It uses control vertices (CVs) and its “polygon” for shaping
It is incredibly smooth
Shaping and managing it is very easy (bunch of lines)

18. Style Spline solve states
NEW in 2016!
It can be a Bezier curve, or a B-spline of 3, 5 or 7 degree
Bezier curves are the smoothest, yet hardest to shape
B-splines of lower degree shape easily, but are not as smooth
Trade off between ease of use vs. quality

19. B-Spline mathematical makeup1 2 3 4
Degree = 3
Spans = 4
4 cubic polynomials
Want more control? We need more polynomials!

20. Using both curves Takes the best of each curve Create using Spline
Convert to Style Spline
Continue editing

21. Summary Continuity is important for smooth geometry
Conics are robust curves with very good continuity
The Style Spline maintains the highest level of internal continuity
The Spline can create complex shapes quickly but can compromise continuity