Answer and Explanation:
(A) The equation of the bi-quadratic Bezier patch is given by:
B(u,v) = sum[i=0 to 2] sum[j=0 to 2] P(i,j) * B2(i,u) * B2(j,v)
where:
- B(u,v) represents the point on the Bezier surface.
- P(i,j) represents the control points of the patch.
- B2(i,u) and B2(j,v) are the quadratic Bezier blending functions defined as B2(i,u) = (1-u)^2, u^2, and 2u(1-u) for i=0,1,2, respectively.
(B) The initial raw material, form, heating source, and support requirements for the rapid prototyping (RP) techniques SLS (Selective Laser Sintering), SLA (Stereolithography), FDM (Fused Deposition Modeling), and LOM (Laminated Object Manufacturing) are as follows:
1. SLS (Selective Laser Sintering):
- Initial Raw Material: Powdered thermoplastic or metal material.
- Form: Fine powder.
- Heating Source: High-powered laser.
- Support Requirements: Typically, SLS does not require support structures as the unsintered powder acts as support.
2. SLA (Stereolithography):
- Initial Raw Material: Liquid photopolymer resin.
- Form: Liquid.
- Heating Source: Ultraviolet (UV) laser or light source.
- Support Requirements: SLA may require support structures to hold up overhanging parts during the printing process. These supports are typically designed to be easily removable after printing.
3. FDM (Fused Deposition Modeling):
- Initial Raw Material: Thermoplastic filament.
- Form: Solid filament.
- Heating Source: Heated extrusion nozzle.
- Support Requirements: FDM requires support structures for overhanging features. These supports are printed alongside the main object and are typically removed manually after printing.
4. LOM (Laminated Object Manufacturing):
- Initial Raw Material: Sheet material, such as paper or plastic.
- Form: Stacked sheets.
- Heating Source: Heated roller or laser.
- Support Requirements: LOM does not require support structures as the unbound material acts as support and is removed after printing.
These are the general characteristics of each RP technique, but it's important to note that specific machines and materials may have variations in their requirements and capabilities.