PhysSandbox
Classical MechanicsWaves & SoundElectricity & MagnetismOptics & LightGravity & OrbitsLabs
🌙Astronomy & The Sky🌡️Thermodynamics🌍Biophysics, Fluids & Geoscience📐Math Visualization🔧Engineering🧪Chemistry

More from Math Visualization

Other simulators in this category — or see all 61.

View category →
NewSchool

Convex Hull (Graham & QuickHull)

Click to add points, drag to move; Graham scan with step playback or QuickHull divide-by-farthest; compare vertex sets.

Launch Simulator
NewSchool

Delaunay & Voronoi

Bowyer–Watson triangulation and dual Voronoi tessellation; click to add seeds, drag to move.

Launch Simulator
NewUniversity / research

Physarum Slime (Agents)

~4500 agents follow a deposited chemoattractant: deposit + diffusion + decay + 3-sensor steering grow path networks.

Launch Simulator
NewSchool

Savitzky–Golay Smoothing

Noisy cosine vs SG(7,2) convolution — preserves peaks better than a wide boxcar.

Launch Simulator
NewSchool

Markov Chain (Weather)

Sun/Rain two-state chain: P matrix, stationary π, empirical vs theory.

Launch Simulator
NewSchool

Gradient Descent (2D)

Level sets of f(x,y) and path (x,y) ← (x,y) − η∇f; bowl or elliptic well.

Launch Simulator
PhysSandbox

Interactive physics, chemistry, and engineering simulators for students, teachers, and curious minds.

Physics

  • Classical Mechanics
  • Waves & Sound
  • Electricity & Magnetism

Science

  • Optics & Light
  • Gravity & Orbits
  • Astronomy & The Sky

More

  • Thermodynamics
  • Biophysics, Fluids & Geoscience
  • Math Visualization
  • Engineering
  • Chemistry

© 2026 PhysSandbox. Free interactive science simulators.

PrivacyTermsContact
Home/Math Visualization/Bézier & de Casteljau

Bézier & de Casteljau

This interactive simulator explores Bézier & de Casteljau in Math Visualization. Drag control points; live recursive linear-interpolation scaffolding evaluates B(t). Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Math Visualization.

Key terms

  • zier
  • casteljau
  • bezier de casteljau
  • math
  • visualization

Curve & parameter

0.5
0.4

Presets

Shortcuts

  • •Drag any Pᵢ to reshape the curve

Measured values

Bézier degree n3
control points4
t0.500

How it works

Bézier curves are everywhere in graphics, fonts and CAD. The de Casteljau algorithm evaluates B(t) by repeated linear interpolation: take each pair of adjacent control points, slide a fraction *t* along the segment, and you get a new — shorter — control polygon. Iterate until a single point remains. It is numerically stable, geometric, and reveals beautiful scaffolding — drag any Pᵢ to reshape the curve in real time.

Key equations

B(t) = Σᵢ C(n,i) (1−t)ⁿ⁻ⁱ tⁱ Pᵢ
de Casteljau: Pᵢ⁾ʳ⁾ = (1−t)Pᵢ⁾ʳ⁻¹⁾ + t Pᵢ₊₁⁾ʳ⁻¹⁾
B(t) = P₀⁾ⁿ⁾, cost: O(n²)