By M. M. Novak (auth.)
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Additional info for Advanced Graphics with the Commodore 128
There, R was the radius of a circle and A the angle. Far more intricate curves can be created using the polar system. 9. 10. 9 Line plotting or point plotting? All the simple programs in this chapter created a screen display by working out the coordinates of each and every point. Clearly, such a task is laborious and causes unnecessary delays. Whenever possible, we shall use the graphic primitives available on the C-128, to DRAw lines and other regular shapes. The line-plotting routine involves the efficient algorithm (much better than we could ever develop with BASIC), thus leading to fast execution.
The first number refers to the row and the second to the column of a matrix. Thus, M32 is an element in the second column of the third row. 54 Advanced Graphics with the Commodore 128 We now define some mathematical operations that can be done with matrices. We say that an operation is performed on a matrix through its elements. Then we can assert that two matrices are equal if all the corresponding elements are also equal. That is, matrices K and L are equal if Kii = Lii where i andj are subscripts.
The resultant vector is defined by the starting point of the first vector and the endpoint of the second vector. More than two vectors can be added in the same way. 5. 5 Vector subtraction As subtraction is, in fact, addition with the opposite sign, the vector addition rules just mentioned can be applied directly. Using vectors a and b again, the vector c = b - a has the components Cy =by- ay Geometry in Two Dimensions 23 Unit vector and scalar multiple A directed line segment of unit length is known as the unit vector.
Advanced Graphics with the Commodore 128 by M. M. Novak (auth.)