bezier-curves

Figma Persona 2022: What’s your creative collaboration style? | Figma Blog (opens in new tab)

Figma Persona 2022 presents a playful quiz designed to help people reflect on their creative collaboration and working styles. Based on 21 questions across problem-solving, workspace habits, and collaboration, the quiz assigns one of eight Figma-inspired personas. The article encourages teams to use these insights to improve communication, planning, and creative collaboration. ## The Figma Persona Quiz - The quiz is intended as an end-of-year reflection and goal-setting exercise. - It evaluates three areas: - How someone generates ideas and solves problems - How they organize their workspace and use tools - How they collaborate with others - Results fall into eight personas: - Lone Ascender - Canvas Captain - Direct Mobilizer - Artful Detacher - Bounding Boxer - Branch Merger - Vector Networker - Bézier Curve Baller ## Organized Individualists - Organized individualists prefer: - Tidy processes and clear deliverables - Defined milestones and structured workflows - Working independently before regrouping - Async updates and bug bashes - They are most effective when given space to develop ideas and solutions. - Collaborators should provide clear expectations, async pre-work, and precise requests. ## The Lone Ascender - The Lone Ascender is described as an organized, analytical individualist. - This persona excels at: - Solving complex problems - Building tactical, practical, systems-driven solutions - Applying consistent processes - Scaling difficult or complicated work - Lone Ascenders favor pragmatism and systematic thinking over idealism. - They value occasional collaboration but may be protective of file organization and formatting. - Suggested tools and habits include: - Memorizing shortcut keys and quick actions - Using FigJam templates to extend structured workflows - Applying strong organizational systems within Figma Overall, Figma frames the personas as a lighthearted way to recognize different working preferences. The practical recommendation is to use the results as a conversation starter, giving teammates the structure, independence, or collaboration style that helps them do their best work.

Desperately seeking squircles | Figma Blog (opens in new tab)

Figma engineer Daniel Furse describes the search for an accurate mathematical model of Apple’s iOS “squircle” shape. The project illustrates Charles Eames’s idea that good design depends on recognizing and working enthusiastically within constraints. Although a superellipse initially appeared to be the answer, careful comparison showed that it was only an approximation, prompting further investigation into Bézier-based constructions. ## Design Through Constraints - Eames defined design as “a plan for arranging elements to accomplish a particular purpose.” - Furse applies this principle to engineering, where code must balance: - Time - Simplicity - Maintainability - Aesthetic quality - The squircle project became a mathematical example of design involving research, false starts, hidden constraints, and refinement. ## Why Squircles Look Different - Apple’s iOS 7 icons replaced conventional rounded squares with more organic-looking squircles. - A rounded square has an abrupt transition between its straight edges and curved corners. - A squircle has continuous curvature around its perimeter, producing a smoother, more unified appearance. - Similar curvature continuity appears in industrial design, such as MacBook corners and earbud cases, where it prevents harsh changes in reflected highlights. ## Modeling the Shape with a Superellipse - To add squircles to Figma, the team needed a precise mathematical description. - Early research suggested that Apple’s shape was a superellipse, a generalized ellipse described by parameters `a`, `b`, and `n`. - With `n = 2`, the formula produces an ellipse; with equal axes, it produces a circle. - Increasing `n` makes the shape increasingly resemble a rounded rectangle, approaching a sharp-cornered rectangle as `n` approaches infinity. - A value around `n = 5` produced an image that looked very similar to an iOS squircle. ## The First False Start - Despite its visual similarity, the superellipse did not match Apple’s actual icon geometry. - Detailed follow-up analysis found a small but consistent discrepancy for every value of `n`. - This meant that simply approximating the superellipse with Bézier curves would not produce the authentic shape. - The investigation therefore moved toward alternative constructions, including sequences of Bézier curves for the corners. The main lesson is that visual resemblance is not enough when reproducing a design precisely: mathematical elegance must be tested against the real artifact, and constraints often reveal the need for a more complex solution.

Delete and Heal for Vector Networks | Figma Blog (opens in new tab)

Figma’s “delete and heal” feature removes a vertex while preserving the surrounding shape as much as possible. What begins as a simple graph-editing operation becomes complex for curved segments and vector networks, where vertices may connect to many edges. Figma addresses this by fitting replacement Bézier curves and pairing edges according to their geometry. ## Basic Deletion and Healing - Standard deletion removes the selected vertex, its incident edges, and any fills that depend on those edges. - “Delete and heal” instead attempts to connect the neighboring vertices. - If a vertex touches only one edge, that edge is removed because no meaningful healing is possible. - Triangles and other small paths require special-case decisions about whether healing produces one edge or multiple edges. - The behavior differs between open and closed paths. ## Preserving Curvature - Curved segments are represented as cubic Bézier curves. - Deleting a vertex joins two cubic curves into one replacement curve. - Figma keeps the original endpoints fixed but adjusts the neighboring control handles to preserve the original curvature. - The algorithm: - Samples points along both original Bézier curves. - Treats the shared vertex as a single point. - Fits a new cubic Bézier curve through the resulting samples. - Figma uses a curve-fitting technique from Philip J. Schneider’s “An Algorithm for Automatically Fitting Digitized Curves,” published in *Graphics Gems*. ## Healing Vector Networks - Unlike traditional path-based editors, Figma models vector objects as undirected multigraphs with edge identity. - A vertex can therefore have more than two incident edges. - If the vertex has an odd number of connected edges, Figma removes all incident edges because no complete pairing is possible. - With an even number of edges, the edges are paired and replaced with new edges. - To determine which edges are “opposite,” the incident edges are sorted by their angles around the deleted vertex. - This graph-based approach allows delete-and-heal to work on branching vector networks, not just simple paths. Figma’s implementation combines graph topology, geometric pairing, Bézier sampling, and curve fitting to make deletion feel intuitive while retaining as much of the original design as possible.

Introducing Vector Networks | Figma Blog (opens in new tab)

Figma’s vector networks replace the traditional path model with a more flexible structure that lets users connect, split, and manipulate geometry naturally. The system remains compatible with existing cubic Bézier curves while improving direct editing, strokes, and fills. The result is a vector tool that behaves more like physical drawing and avoids several long-standing limitations of pen-based editors. ## Vector Networks vs. Traditional Paths - Traditional paths are chains of lines and curves connecting two endpoints. - Vector networks allow lines and curves between any points, without requiring one continuous chain. - Users can: - Connect any points together - Delete geometry anywhere - Split and recombine shapes naturally - Attach three or more lines to a single point - Stroke caps and joins work consistently, including at multi-line junctions. ## Direct Curve Manipulation - Existing vector tools typically use cubic Bézier curves with control handles positioned away from the curve. - Figma preserves Bézier compatibility but adds a bend tool for direct manipulation. - Holding Command on macOS allows users to drag the curve itself. - Figma automatically adjusts the underlying control handles to match the desired bend. ## More Intuitive Fills - Traditional vector engines use the winding number rule, where fill behavior depends on curve direction. - This makes fills difficult to understand because users generally cannot see whether curves were drawn clockwise or counterclockwise. - Vector networks automatically fill enclosed regions. - A paint bucket-style tool lets users toggle individual enclosed areas to create holes directly. - Developing this fill system was the most difficult part because earlier approaches required users to manually manage negative space. ## Design Through Iteration - Figma’s team initially explored more advanced curve types but chose to remain compatible with existing vector formats. - User studies showed that many people did not consciously notice vector networks; they simply found the tool behaved as expected. - The contrast became clear when users returned to conventional vector editors and encountered their limitations. - Despite many abandoned approaches and doubts during development, Figma concluded that vector networks offered a meaningful improvement over paths. Figma’s recommendation is implicit: vector editing should prioritize direct manipulation and intuitive geometry rather than forcing users to understand the underlying path mechanics. Vector networks preserve compatibility while making drawing, editing, strokes, and fills substantially more natural.