- Curves and splines are fundamental tools in multimedia graphics for creating smooth shapes, animations, paths, and surfaces.
- Curves and splines allow designers and developers to model complex forms using mathematical functions instead of manually drawing every detail.
Curves
- A curve is a continuous and smooth line defined mathematically.
- In computer graphics, curves are used:-
- In the making of the logo and font design.
- In Character Modeling
- In animation paths
- In UI/UX shapes
- In motion graphics
- In 3D surface modeling
Types of Curves in Graphics
A. Parametric Curves
- It is a curve defined using a parameter (usually t, where 0 ≤ t ≤ 1).
- For example-
x=f(t), y=g(t)
- Advantages
- This curve is easy to compute.
- This curve can be a smooth representation.
- This curve is Ideal for animation.
B. Bézier Curves
- It is one of the most widely used curves in multimedia applications.
-
The Bezier curve starts at the first control point and ends at the last control point.Shape influenced by intermediate control pointsLies within convex hull of control points
- It is used in-
- Adobe Illustrator
- Font design (TrueType)
- SVG graphics
- Animation paths
- Types of Bezier Curves:
-
- Linear Bezier Curves (2 control points)
- This Bezier curve has 2 control points.
- Quadratic Bezier Curves (3 control points)
- This Bezier curve has 3 control points.
- Cubic Bezier Curves
- This Bezier curve has 4 control points.
- This is the most common type of Bezier Curve.
- Linear Bezier Curves (2 control points)
Cubic Bézier equation:
𝑃
(
𝑡
)
=
(
1
−
𝑡
)
3
𝑃
0
+
3
𝑡
(
1
−
𝑡
)
2
𝑃
1
+
3
𝑡
2
(
1
−
𝑡
)
𝑃
2
+
𝑡
3
𝑃
3
P(t)=(1−t)
3
P
0
+3t(1−t)
2
P
1
+3t
2
(1−t)P
2
+t
3
P
3
🔹 C. B-Spline Curves (Basis Splines)
More flexible than Bézier curves.
Features:
Local control (moving one control point affects only part of curve)
Smooth transitions
Can create complex shapes
Used in:
CAD systems
3D modeling
Animation tools
🔹 D. NURBS (Non-Uniform Rational B-Splines)
Advanced form of B-Splines.
Advantages:
Can represent circles and complex shapes exactly
Used in professional 3D modeling
Used in:
Maya
AutoCAD
3D animation and industrial design
3️⃣ What Are Splines?
Originally, a spline was a flexible strip used by shipbuilders to draw smooth curves.
In graphics, a spline is:
A smooth curve defined by multiple polynomial segments joined together with continuity conditions.
4️⃣ Types of Splines
🔹 1. Interpolating Splines
Curve passes through all control points.
Used when exact data fitting is required.
Example:
Animation keyframe interpolation
🔹 2. Approximating Splines
Curve does not necessarily pass through control points.
Provides smoother control.
Example:
Bézier and B-Splines
🔹 3. Hermite Splines
Defined using:
Endpoints
Tangent vectors
Used in:
Animation motion control
Game development
5️⃣ Continuity in Curves
Continuity determines smoothness where curve segments join.
C⁰ continuity – Curves meet
C¹ continuity – Tangent continuity (smooth)
C² continuity – Curvature continuity (very smooth)
Higher continuity = smoother visual appearance.
6️⃣ Applications in Multimedia Graphics
🎬 Animation
Character movement paths
Camera motion
Keyframe interpolation
🎨 Graphic Design
Vector illustrations
Font outlines
Logo design
🎮 Game Development
Racing tracks
Object trajectories
Terrain modeling
🧱 3D Modeling
Surface generation (sweeps, lofts)
Organic shapes
7️⃣ Why Curves & Splines Are Important
✔ Reduce memory usage
✔ Provide smooth shapes
✔ Easy to edit and modify
✔ High precision modeling
✔ Essential for modern UI and animation
0 Comments