• for P₀, (1 - u)³
• for P₁, 3u(1 - u)²
• for P₂, 3u²(1 - u)
• for P₃, u³

Calculate the exact value of the coordinates of the curve at u = 1/2. Using this information and what you know about how the slope of the curve must behave at the endpoints, draw a reasonably accurate picture of the entire curve from P₀ to P₃.

4. This question focuses on clipping the five-sided polygon shown below against the upper edge of the rectangular window. The Sutherland-Hodgeman polygon clipping algorithm creates a single polygon and in this case will produce a spurious line along part of the upper boundary. The Weiler-Atherton algorithm can build more than one polygon and does not leave a spurious line. Show how the Weiler-Atherton algorithm traces the appropriate boundaries as it moves around the polygon and window edge, starting at vertex V₁. Only consider clipping against the upper window edge in this question.

5. The equation below represents a variety of contributions to the illumination for a point on a surface. The equation takes into account the surface properties, the light sources and their direction, as well as the direction of viewing. Explain the nature and significance of the various terms, and draw vector diagrams as needed to help clarify your explanation.

I = k_dI_a + k_dI_l(N ^. L) + k_sW(theta)I_lcosⁿ(phi)

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