.NORM LDA XX15 \ Fetch the x-coordinate into A JSR SQUA \ Set (A P) = A * A = x^2 STA R \ Set (R Q) = (A P) = x^2 LDA P STA Q LDA XX15+1 \ Fetch the y-coordinate into A JSR SQUA \ Set (A P) = A * A = y^2 STA T \ Set (T P) = (A P) = y^2 LDA P \ Set (R Q) = (R Q) + (T P) = x^2 + y^2 ADC Q \ STA Q \ First, doing the low bytes, Q = Q + P LDA T \ And then the high bytes, R = R + T ADC R STA R LDA XX15+2 \ Fetch the z-coordinate into A JSR SQUA \ Set (A P) = A * A = z^2 STA T \ Set (T P) = (A P) = z^2 LDA P \ Set (R Q) = (R Q) + (T P) = x^2 + y^2 + z^2 ADC Q \ STA Q \ First, doing the low bytes, Q = Q + P LDA T \ And then the high bytes, R = R + T ADC R STA R JSR LL5 \ We now have the following: \ \ (R Q) = x^2 + y^2 + z^2 \ \ so we can call LL5 to use Pythagoras to get: \ \ Q = SQRT(R Q) \ = SQRT(x^2 + y^2 + z^2) \ \ So Q now contains the length of the vector (x, y, z), \ and we can normalise the vector by dividing each of \ the coordinates by this value, which we do by calling \ routine TIS2. TIS2 returns the divided figure, using \ 96 to represent 1 and 96 with bit 7 set for -1 LDA XX15 \ Call TIS2 to divide the x-coordinate in XX15 by Q, JSR TIS2 \ with 1 being represented by 96 STA XX15 LDA XX15+1 \ Call TIS2 to divide the y-coordinate in XX15+1 by Q, JSR TIS2 \ with 1 being represented by 96 STA XX15+1 LDA XX15+2 \ Call TIS2 to divide the z-coordinate in XX15+2 by Q, JSR TIS2 \ with 1 being represented by 96 STA XX15+2 .NO1 RTS \ Return from the subroutineName: NORM [Show more] Type: Subroutine Category: Maths (Geometry) Summary: Normalise the three-coordinate vector in XX15 Deep dive: Tidying orthonormal vectors Orientation vectorsContext: See this subroutine in context in the source code References: This subroutine is called as follows: * TIDY calls NORM

We do this by dividing each of the three coordinates by the length of the vector, which we can calculate using Pythagoras. Once normalised, 96 (&E0) is used to represent a value of 1, and 96 with bit 7 set (&E0) is used to represent -1. This enables us to represent fractional values of less than 1 using integers. Arguments: XX15 The vector to normalise, with: * The x-coordinate in XX15 * The y-coordinate in XX15+1 * The z-coordinate in XX15+2 Returns: XX15 The normalised vector Q The length of the original XX15 vector Other entry points: NO1 Contains an RTS

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Subroutine LL5 (category: Maths (Arithmetic))

Calculate Q = SQRT(R Q)

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Subroutine SQUA (category: Maths (Arithmetic))

Clear bit 7 of A and calculate (A P) = A * A

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Subroutine TIS2 (category: Maths (Arithmetic))

Calculate A = A / Q