Give an algorithm for drawing the part of a circle which lies in the first octant....

 

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Give an algorithm for drawing the part of a circle which lies in the first octant. Assume that the circle has integer radius and is centered at the origin. Assume that you have a function setpixel(x, y) which turns on pixel (x, y). [10 marks] Derive a matrix, or a product of matrices, to perform a clockwise 2D rotation of arbitrary angle, 0, about an arbitrary point, (c, yc). [4 marks] Provide an algorithm to ascertain whether the Bezier curve defined by PP2P3P lies within some tolerance, e, of the straight line segment, PP, which joins the Bezier curve's end points. Your algorithm must return false if the Bezier curve is outside the tolerance; it must return true if the curve is well inside the tolerance; it may return either true or false if the curve is inside, but not well inside, the tolerance. [6 marks] Give an algorithm for drawing the part of a circle which lies in the first octant. Assume that the circle has integer radius and is centered at the origin. Assume that you have a function setpixel(x, y) which turns on pixel (x, y). [10 marks] Derive a matrix, or a product of matrices, to perform a clockwise 2D rotation of arbitrary angle, 0, about an arbitrary point, (c, yc). [4 marks] Provide an algorithm to ascertain whether the Bezier curve defined by PP2P3P lies within some tolerance, e, of the straight line segment, PP, which joins the Bezier curve's end points. Your algorithm must return false if the Bezier curve is outside the tolerance; it must return true if the curve is well inside the tolerance; it may return either true or false if the curve is inside, but not well inside, the tolerance. [6 marks]

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