3D-MIDTERM PDF - Bezier, NURBS, and More

# Bezier Curves - A French engineer, Pierre Bézier, was one of the first to use splines to generate smooth curves. - Bézier curves are known as "paths" and are smooth. ## Anatomy of a Bezier Curve - **Control Points** define the shape of the curve, and are similar to vertices in mesh objects. The...

# Bezier Curves - A French engineer, Pierre Bézier, was one of the first to use splines to generate smooth curves. - Bézier curves are known as "paths" and are smooth. ## Anatomy of a Bezier Curve - **Control Points** define the shape of the curve, and are similar to vertices in mesh objects. The curve intersects with each control point. - **Control Point Handles** are a pair of handles associated with each control point that allow you to control the rotation and curve influence of the control point. - **Curve Segments** are defined by the mathematical relationship between two control points. ## Editing Bezier Curves - The handles of the control points are the most defining aspect of Bézier curves. - Each control point has two handles. - When you select the control point, you also select both of its handles. ## NURBS (Non-Uniform Rational B-Spline) - NURBS curves have **no handles**. - Control points for NURBS curves **do not normally 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. They can be modified interactively after their creation. ## Properties of a NURBS Curve - **Control Point Weight** influences how much the control point effects the curve. - **Knots** are vectors that describe how control points effect the curve's overall shape. - **Order** determines how the curve follows the lines between control points. A lower order means the curve follows the lines closely, while a higher order makes the curve smoother. ## NURBS Surfaces - NURBS surfaces or "patches" are created when a NURBS curve is extruded or when two or more curves are joined together in 3D space. - These NURBS patches can be used to slowly build up a 3D model. ## Sweeping Techniques - **Lathe (Revolve):** This technique creates a 3D surface by revolving a 2D shape on an axis, producing a symmetrical form. This is often referred to as a "surface revolution". - **Lofting:** Involves creating a complex 3D object using two 2D objects, such as curves and splines. ## Subdivision Modeling - Refers to the process of repeatedly dividing a form into smaller subdivisions. ## Materials - **Color:** Defines the basic RGB color of a material, which is used in all subsequent calculations. - **Alpha/Transparency:** Controls how much light passes through the material. A lower value means more transparency. - **Refraction (IOR):** Represents the bending of light as it passes through a material, like glass. - **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, creating highlights. - **Reflection:** Determines how much light is reflected from the environment surrounding the object, creating mirror-like effects. - **Luminosity/Emission:** Controls the amount of light emitted by an object, such as a lightbulb or fire. - **Subsurface Scattering:** Simulates light scattering within a material, creating realistic effects like the appearance of skin or a lit hand. ## Texture - A 2D image applied to a 3D object to enhance its appearance, like a texture map. - Common file formats include JPEG, PNG, and TIFF. ## Procedural Textures - A texture created algorithmically, often used to generate repetitive patterns or effects. ## Noise - A procedural texture that adds randomness to a 2D image. - Common types of noise include Fractals, Perlin Noise, and Marble Noise. ## Gradient Generators - A procedural texture that creates a gradual transition between colors. ## Bump Mapping - A technique that creates the illusion of depth and texture by altering the normal vectors of a surface. This is a less computationally intensive technique, but the details are fake. - **Bump Only:** Simulates the creation of bumps and indentations on the surface. - **Normal Only:** Provides a more refined level of detail and visual fidelity. - **Normal + Displacement:** Combines the benefits of bump and normal maps to create the most realistic and detailed results. ## Displacement Maps - A technique that actually modifies the geometry of a 3D model, resulting in actual depth and displacement. - While more computationally intensive, it offers a higher level of realism.