Skip to navigation

BBC Micro Elite

Maths (Geometry): LL51

Name: LL51 [View in context] Type: Subroutine Category: Maths (Geometry) Summary: Calculate the dot product of XX15 and XX16
Calculate following dot products: XX12(1 0) = XX15(5 0) . XX16(5 0) XX12(3 2) = XX15(5 0) . XX16(11 6) XX12(5 4) = XX15(5 0) . XX16(12 17) storing the results as sign-magnitude numbers in XX12 through XX12+5. When called from part 5 of LL9, XX12 contains the vector [x y z] to the ship we're drawing, and XX16 contains the orientation vectors, so it returns: [ x ] [ sidev_x ] [ x ] [ roofv_x ] [ x ] [ nosev_x ] [ y ] . [ sidev_y ] [ y ] . [ roofv_y ] [ y ] . [ nosev_y ] [ z ] [ sidev_z ] [ z ] [ roofv_z ] [ z ] [ nosev_z ] When called from part 6 of LL9, XX12 contains the vector [x y z] of the vertex we're analysing, and XX16 contains the transposed orientation vectors with each of them containing the x, y and z elements of the original vectors, so it returns: [ x ] [ sidev_x ] [ x ] [ sidev_y ] [ x ] [ sidev_z ] [ y ] . [ roofv_x ] [ y ] . [ roofv_y ] [ y ] . [ roofv_z ] [ z ] [ nosev_x ] [ z ] [ nosev_y ] [ z ] [ nosev_z ] Arguments: XX15(1 0) The ship (or vertex)'s x-coordinate as (x_sign x_lo) XX15(3 2) The ship (or vertex)'s y-coordinate as (y_sign y_lo) XX15(5 4) The ship (or vertex)'s z-coordinate as (z_sign z_lo) XX16 to XX16+5 The scaled sidev (or _x) vector, with: * x, y, z magnitudes in XX16, XX16+2, XX16+4 * x, y, z signs in XX16+1, XX16+3, XX16+5 XX16+6 to XX16+11 The scaled roofv (or _y) vector, with: * x, y, z magnitudes in XX16+6, XX16+8, XX16+10 * x, y, z signs in XX16+7, XX16+9, XX16+11 XX16+12 to XX16+17 The scaled nosev (or _z) vector, with: * x, y, z magnitudes in XX16+12, XX16+14, XX16+16 * x, y, z signs in XX16+13, XX16+15, XX16+17 Returns: XX12(1 0) The dot product of [x y z] vector with the sidev (or _x) vector, with the sign in XX12+1 and magnitude in XX12 XX12(3 2) The dot product of [x y z] vector with the roofv (or _y) vector, with the sign in XX12+3 and magnitude in XX12+2 XX12(5 4) The dot product of [x y z] vector with the nosev (or _z) vector, with the sign in XX12+5 and magnitude in XX12+4
.LL51 LDX #0 \ Set X = 0, which will contain the offset of the vector \ to use in the calculation, increasing by 6 for each \ new vector LDY #0 \ Set Y = 0, which will contain the offset of the \ result bytes in XX12, increasing by 2 for each new \ result .ll51 LDA XX15 \ Set Q = x_lo STA Q LDA XX16,X \ Set A = |sidev_x| JSR FMLTU \ Set T = A * Q / 256 STA T \ = |sidev_x| * x_lo / 256 LDA XX15+1 \ Set S to the sign of x_sign * sidev_x EOR XX16+1,X STA S LDA XX15+2 \ Set Q = y_lo STA Q LDA XX16+2,X \ Set A = |sidev_y| JSR FMLTU \ Set Q = A * Q / 256 STA Q \ = |sidev_y| * y_lo / 256 LDA T \ Set R = T STA R \ = |sidev_x| * x_lo / 256 LDA XX15+3 \ Set A to the sign of y_sign * sidev_y EOR XX16+3,X JSR LL38 \ Set (S T) = (S R) + (A Q) STA T \ = |sidev_x| * x_lo + |sidev_y| * y_lo LDA XX15+4 \ Set Q = z_lo STA Q LDA XX16+4,X \ Set A = |sidev_z| JSR FMLTU \ Set Q = A * Q / 256 STA Q \ = |sidev_z| * z_lo / 256 LDA T \ Set R = T STA R \ = |sidev_x| * x_lo + |sidev_y| * y_lo LDA XX15+5 \ Set A to the sign of z_sign * sidev_z EOR XX16+5,X JSR LL38 \ Set (S A) = (S R) + (A Q) \ = |sidev_x| * x_lo + |sidev_y| * y_lo \ + |sidev_z| * z_lo STA XX12,Y \ Store the result in XX12+Y(1 0) LDA S STA XX12+1,Y INY \ Set Y = Y + 2 INY TXA \ Set X = X + 6 CLC ADC #6 TAX CMP #17 \ If X < 17, loop back to ll51 for the next vector BCC ll51 RTS \ Return from the subroutine