Bézier and NURBS Curves in Graphics

Study Notes

Bézier curves, named after French engineer Pierre Bézier, are smooth curves used in computer graphics.
Bézier curves are defined by control points and their associated handles.
Control points define the shape of the curve and the curve intersects with each control point.
Control point handles influence the rotation and curve influence of the control point.
A Bézier curve is made up of segments, defined by the mathematical relationship between two control points.

The handles of the control points are key to editing Bézier curves.
Each control point has two handles, and selecting a control point also selects both of its handles.

NURBS curves are a type of spline that differ from Bézier curves by having no handles.
Control points for NURBS curves do not touch the curve shape.
Control points in NURBS are weighted to influence the shape of the curve.
NURBS curves are advantageous because they can create complex 3D shapes and surfaces and can be modified in 3D space.

Control Point Weight: Influences how much a control point affects the curve.
Knots: Vectors that describe how control points effect the curve's overall shape.
Order: Determines the curve’s smoothness. A lower order means the curve follows the lines between control points closely, while a higher order smooths the curve further.

NURBS surfaces, also known as patches, are created by extruding a NURBS curve or joining multiple curves in 3D space.
NURBS patches build up a 3D model gradually.

Lathe (Revolve): Creates a 3D surface by revolving a 2D shape on an axis, producing a symmetrical form. This is often called a "surface revolution".
Lofting: Creates a complex 3D object using two 2D objects, such as curves and splines.

Refers to repeatedly dividing a form into smaller subdivisions to create complex shapes.

Color: Defines the RGB color of a material.
Alpha/ Transparency: Controls how much light passes through a material. A lower value means more transparency.
Refraction (IOR): Represents the bending of light as it passes through a material.
Gloss: Simulates a shiny, reflective surface, often used for materials like wood or stone.
Specular: Defines how much light is reflected directly from a light source.
Reflection: Determines how much light is reflected from the environment surrounding the object.
Luminosity/Emission: Controls the amount of light emitted by an object.
Subsurface Scattering: Simulates light scattering within a material.

A texture generated algorithmically, often used to generate repetitive patterns or effects.

A technique that creates the illusion of depth and texture by altering the normal vectors of a surface.
Bump Only: Simulates bumps and indentations.
Normal Only: Provides a more detailed level of detail and visual fidelity.
Normal + Displacement: Combines the benefits of bump and normal maps to create the most realistic and detailed results.

A technique that modifies the geometry of a 3D model to create actual depth and displacement.
This technique is more computationally intensive but offers the highest level of realism.