Smooth Sketching Understanding splines in the SOLIDWORKS sketcher

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

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)

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?

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

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

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

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

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

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

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

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

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

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”

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

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!

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)

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

B-Spline mathematical makeup 1 2 3 4 Degree = 3 Spans = 4 4 cubic polynomials Want more control? We need more polynomials!

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

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