Computer Graphics

Numerical Analysis · Axiom Academy

REAL WORLD Computer Graphics Applications How interpolation shapes the digital visual world REAL WORLD Interpolation in Computer Graphics Nearly every curve, surface, and animation you see on screen uses interpolation techniques. From the fonts you're reading to game animations, these mathematical tools are everywhere. Bezier curves define letter shapes Smooth motion between keyframes Curved surfaces from control points Font Design with Bezier Curves Every scalable font (TrueType, OpenType) uses Bezier curves to define letter outlines. This allows fonts to scale smoothly to any size. PostScript and TrueType fonts use quadratic (degree 2) or cubic (degree 3) Bezier curves. A typical letter might use 10-50 control points. Animators set keyframes at specific times, and interpolation fills in the frames between. The type of interpolation determines the motion's feel. NURBS (Non-Uniform Rational B-Splines) extend spline curves to surfaces, creating smooth 3D models from control point grids. CAD software - Designing car bodies, aircraft Game development - Character models, terrain Visual effects - Creature design, environments Product design - Consumer electronics, furniture When you resize an image, interpolation determines pixel values at non-integer coordinates. Higher-quality methods use more neighboring pixels.

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