MSFD Trigonometry script - fast sine and cosine
I asked JDGBOLT to share his latest, greatest trigonometry script with the readers of MSFD, and I am happy to present it here. Although it is very long, I believe this will be an invaluable resource for anyone doing scripts involving trigonometry, e.g. those involving directional movement. I have edited and commented the original script to make it easy to use for any modder. Please give JDGBOLT credit if you use this!
The script calculates the sine and cosine of three angles. These will usually be the angles of all three axes of an object, obtained with GetAngle. Store these angles in the global variables
float Z_input_variable
float X_input_variable
float _input_variable
You can do this e.g. from another script on the object you are moving. Then run the script: Startscript jdtrigscript. The script in this version is self-terminating and will place the results in the following global variables:
Float Z_sin
Float Z_cos
Float X_sin
Float X_cos
Float Y_sin
Float Y_cos
You need to create all of the global variables before you can compile this script. The script is very fast, and the results very precise. The results will be available after one frame.
(Extra thanks to JDGBOLT for sharing his script! By the way, this is the colored script output from MWEdit, see the tip on alternative editors.)
begin jdtrigscript
; by JDGBOLT
; edited and commented for MSFD by GhanBuriGhan
; simultaneous calculation of sine and cosine for three angles (e.g. three different axes)
; for intermediate results of sine and cosine
float ax1
float ax2
float ay1
float ay2
; main angle variable
float angle
;temp storage for angle:
float angle_source ;contains angle (loaded from global)
float angle_temp
float angle_temp2
short angleshort ; short variable to take up angle - for tab values
float angledec ; for decimal portion of angle
short anglequad ;quadrant
float axfinal ; for final result sine
float ayfinal ; for final result cosine
float angconvx1 ; for calculating decimal portion of sine and cosine
float angconvy1
float angconvx2
float angconvy2
short objnum ;counter to calculate all three angles
;-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
while ( objnum <= 3 ) ; this script calculates sine and cosine for all three axis in one frame
;exporting results:
if ( objnum == 1 )
set Z_sin to axfinal ; assign to global var. Z_sin to free axfinal for next axis
set Z_cos to ayfinal ; ditto
endif
if ( objnum == 2 )
set X_sin to axfinal ;ditto
set X_cos to ayfinal ;ditto
endif
if ( objnum == 3 )
set Y_sin to axfinal ;ditto
set Y_cos to ayfinal ;ditto
;MessageBox "sine of Z: %.3f cosine of Z: %.3f", Z_sin, Z_cos
;MessageBox "sine of X: %.3f cosine of X: %.3f", X_sin, X_cos
;MessageBox "sine of Y: %.3f cosine of Y: %.3f", Y_sin, Y_cos
Set objnum to 0
StopScript jdtrigscript
Return
endif
;-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
set objnum to ( objnum + 1 ) ;count up to do all three angles one by one
;-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
; obtain the angles from global variables.
if ( objnum == 1 )
set angle_source to Z_input_angle
endif
if ( objnum == 2 )
set angle_source to X_input_angle
endif
if ( objnum == 3 )
set angle_source to Y_input_angle
endif
;GetAngle returns values from -180 to +180, so we need to compensate for calculation to get
;values from 0 to 360°C:
if ( angle_source < 0 )
set angle_source to ( 360 + angle_source )
endif
set angle to angle_source
;-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
;determine quadrant. This way we need to calculate sine and cosine only for 0-90°
if ( angle <= 90 )
set angle_temp2 to angle
set anglequad to 1
elseif ( angle <= 180 )
set angle_temp2 to ( 180 - angle )
set anglequad to 2
elseif ( angle <= 270 )
set angle_temp2 to ( angle - 180 )
set anglequad to 3
elseif ( angle <= 360 )
set angle_temp2 to ( 360 - angle )
set anglequad to 4
endif
; obtain the decimal part of the angle
set angleshort to angle_temp2
set angledec to ( angle_temp2 - angleshort ) ; the difference between the float and the short is the decimal part
set angle_temp to angleshort
;-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
; These are pre-calculated values for sine and cosine:
if ( angle_temp <= 10 ) ; angles arranged in chunks of 10 for speed (and if block limits?)
if ( angle_temp == 0 )
set ax1 to 0.000000 ; sine
set ay1 to 1.000000 ;cosine
set ax2 to 0.017452 ; sine of angletemp+1
set ay2 to 0.999847 ;cosine of angletemp+1
elseif ( angle_temp == 1 )
set ax1 to 0.017452
set ay1 to 0.999847
set ax2 to 0.034899
set ay2 to 0.999390
elseif ( angle_temp == 2 )
set ax1 to 0.034899
set ay1 to 0.999390
set ax2 to 0.052333
set ay2 to 0.998629
elseif ( angle_temp == 3 )
set ax1 to 0.052333
set ay1 to 0.998629
set ax2 to 0.069756
set ay2 to 0.997564
elseif ( angle_temp == 4 )
set ax1 to 0.069756
set ay1 to 0.997564
set ax2 to 0.087155
set ay2 to 0.996194
elseif ( angle_temp == 5 )
set ax1 to 0.087155
set ay1 to 0.996194
set ax2 to 0.104528
set ay2 to 0.994521
elseif ( angle_temp == 6 )
set ax1 to 0.104528
set ay1 to 0.994521
set ax2 to 0.121869
set ay2 to 0.992546
elseif ( angle_temp == 7 )
set ax1 to 0.121869
set ay1 to 0.992546
set ax2 to 0.139173
set ay2 to 0.990268
elseif ( angle_temp == 8 )
set ax1 to 0.139173
set ay1 to 0.990268
set ax2 to 0.156434
set ay2 to 0.987688
elseif ( angle_temp == 9 )
set ax1 to 0.156434
set ay1 to 0.987688
set ax2 to 0.173648
set ay2 to 0.984807
elseif ( angle_temp == 10 )
set ax1 to 0.173648
set ay1 to 0.984807
set ax2 to 0.190808
set ay2 to 0.981627
endif
elseif ( angle_temp <= 20 ) ; and so on…
if ( angle == 11 )
set ax1 to 0.190808
set ay1 to 0.981627
set ax2 to 0.207911
set ay2 to 0.978147
elseif ( angle_temp == 12 )
set ax1 to 0.207911
set ay1 to 0.978147
set ax2 to 0.224951
set ay2 to 0.974370
elseif ( angle_temp == 13 )
set ax1 to 0.224951
set ay1 to 0.974370
set ax2 to 0.241921
set ay2 to 0.970295
elseif ( angle_temp == 14 )
set ax1 to 0.241921
set ay1 to 0.970295
set ax2 to 0.258819
set ay2 to 0.965925
elseif ( angle_temp == 15 )
set ax1 to 0.258819
set ay1 to 0.965925
set ax2 to 0.275637
set ay2 to 0.961261
elseif ( angle_temp == 16 )
set ax1 to 0.275637
set ay1 to 0.961261
set ax2 to 0.292371
set ay2 to 0.956304
elseif ( angle_temp == 17 )
set ax1 to 0.292371
set ay1 to 0.956304
set ax2 to 0.309016
set ay2 to 0.951056
elseif ( angle_temp == 18 )
set ax1 to 0.309016
set ay1 to 0.951056
set ax2 to 0.325568
set ay2 to 0.945518
elseif ( angle_temp == 19 )
set ax1 to 0.325568
set ay1 to 0.945518
set ax2 to 0.342020
set ay2 to 0.939692
elseif ( angle_temp == 20 )
set ax1 to 0.342020
set ay1 to 0.939692
set ax2 to 0.358367
set ay2 to 0.933580
endif
elseif ( angle_temp <= 30 )
if ( angle_temp == 21 )
set ax1 to 0.358367
set ay1 to 0.933580
set ax2 to 0.374606
set ay2 to 0.927183
elseif ( angle_temp == 22 )
set ax1 to 0.374606
set ay1 to 0.927183
set ax2 to 0.390731
set ay2 to 0.920504
elseif ( angle_temp == 23 )
set ax1 to 0.390731
set ay1 to 0.920504
set ax2 to 0.406736
set ay2 to 0.913545
elseif ( angle_temp == 24 )
set ax1 to 0.406736
set ay1 to 0.913545
set ax2 to 0.422618
set ay2 to 0.906307
elseif ( angle_temp == 25 )
set ax1 to 0.422618
set ay1 to 0.906307
set ax2 to 0.438371
set ay2 to 0.898794
elseif ( angle_temp == 26 )
set ax1 to 0.438371
set ay1 to 0.898794
set ax2 to 0.453990
set ay2 to 0.891006
elseif ( angle_temp == 27 )
set ax1 to 0.453990
set ay1 to 0.891006
set ax2 to 0.469471
set ay2 to 0.882947
elseif ( angle_temp == 28 )
set ax1 to 0.469471
set ay1 to 0.882947
set ax2 to 0.484809
set ay2 to 0.874619
elseif ( angle_temp == 29 )
set ax1 to 0.484809
set ay1 to 0.874619
set ax2 to 0.500000
set ay2 to 0.866025
elseif ( angle_temp == 30 )
set ax1 to 0.500000
set ay1 to 0.866025
set ax2 to 0.515038
set ay2 to 0.857167
endif
elseif ( angle_temp <= 40 )
if ( angle_temp == 31 )
set ax1 to 0.515038
set ay1 to 0.857167
set ax2 to 0.529919
set ay2 to 0.848048
elseif ( angle_temp == 32 )
set ax1 to 0.529919
set ay1 to 0.848048
set ax2 to 0.544639
set ay2 to 0.838670
elseif ( angle_temp == 33 )
set ax1 to 0.544639
set ay1 to 0.838670
set ax2 to 0.559192
set ay2 to 0.829037
elseif ( angle_temp == 34 )
set ax1 to 0.559192
set ay1 to 0.829037
set ax2 to 0.573576
set ay2 to 0.819152
elseif ( angle_temp == 35 )
set ax1 to 0.573576
set ay1 to 0.819152
set ax2 to 0.587785
set ay2 to 0.809016
elseif ( angle_temp == 36 )
set ax1 to 0.587785
set ay1 to 0.809016
set ax2 to 0.601815
set ay2 to 0.798635
elseif ( angle_temp == 37 )
set ax1 to 0.601815
set ay1 to 0.798635
set ax2 to 0.615661
set ay2 to 0.788010
elseif ( angle_temp == 38 )
set ax1 to 0.615661
set ay1 to 0.788010
set ax2 to 0.629320
set ay2 to 0.777145
elseif ( angle_temp == 39 )
set ax1 to 0.629320
set ay1 to 0.777145
set ax2 to 0.642787
set ay2 to 0.766044
elseif ( angle_temp == 40 )
set ax1 to 0.642787
set ay1 to 0.766044
set ax2 to 0.656059
set ay2 to 0.754709
endif
elseif ( angle_temp <= 50 )
if ( angle_temp == 41 )
set ax1 to 0.656059
set ay1 to 0.754709
set ax2 to 0.669130
set ay2 to 0.743144
elseif ( angle_temp == 42 )
set ax1 to 0.669130
set ay1 to 0.743144
set ax2 to 0.681998
set ay2 to 0.731353
elseif ( angle_temp == 43 )
set ax1 to 0.681998
set ay1 to 0.731353
set ax2 to 0.694658
set ay2 to 0.719339
elseif ( angle_temp == 44 )
set ax1 to 0.694658
set ay1 to 0.719339
set ax2 to 0.707106
set ay2 to 0.707106
elseif ( angle_temp == 45 )
set ax1 to 0.707106
set ay1 to 0.707106
set ax2 to 0.719339
set ay2 to 0.694658
elseif ( angle_temp == 46 )
set ax1 to 0.719339
set ay1 to 0.694658
set ax2 to 0.731353
set ay2 to 0.681998
elseif ( angle_temp == 47 )
set ax1 to 0.731353
set ay1 to 0.681998
set ax2 to 0.743144
set ay2 to 0.669130
elseif ( angle_temp == 48 )
set ax1 to 0.743144
set ay1 to 0.669130
set ax2 to 0.754709
set ay2 to 0.656059
elseif ( angle_temp == 49 )
set ax1 to 0.754709
set ay1 to 0.656059
set ax2 to 0.766044
set ay2 to 0.642787
elseif ( angle_temp == 50 )
set ax1 to 0.766044
set ay1 to 0.642787
set ax2 to 0.777145
set ay2 to 0.629320
endif
elseif ( angle_temp <= 60 )
if ( angle == 51 )
set ax1 to 0.777145
set ay1 to 0.629320
set ax2 to 0.788010
set ay2 to 0.615661
elseif ( angle_temp == 52 )
set ax1 to 0.788010
set ay1 to 0.615661
set ax2 to 0.798635
set ay2 to 0.601815
elseif ( angle_temp == 53 )
set ax1 to 0.798635
set ay1 to 0.601815
set ax2 to 0.809016
set ay2 to 0.587785
elseif ( angle_temp == 54 )
set ax1 to 0.809016
set ay1 to 0.587785
set ax2 to 0.819152
set ay2 to 0.573576
elseif ( angle_temp == 55 )
set ax1 to 0.819152
set ay1 to 0.573576
set ax2 to 0.829037
set ay2 to 0.559192
elseif ( angle_temp == 56 )
set ax1 to 0.829037
set ay1 to 0.559192
set ax2 to 0.838670
set ay2 to 0.544639
elseif ( angle_temp == 57 )
set ax1 to 0.838670
set ay1 to 0.544639
set ax2 to 0.848048
set ay2 to 0.529919
elseif ( angle_temp == 58 )
set ax1 to 0.848048
set ay1 to 0.529919
set ax2 to 0.857167
set ay2 to 0.515038
elseif ( angle_temp == 59 )
set ax1 to 0.857167
set ay1 to 0.515038
set ax2 to 0.866025
set ay2 to 0.500000
elseif ( angle_temp == 60 )
set ax1 to 0.866025
set ay1 to 0.500000
set ax2 to 0.874619
set ay2 to 0.484809
endif
elseif ( angle_temp <= 70 )
if ( angle_temp == 61 )
set ax1 to 0.874619
set ay1 to 0.484809
set ax2 to 0.882947
set ay2 to 0.469471
elseif ( angle_temp == 62 )
set ax1 to 0.882947
set ay1 to 0.469471
set ax2 to 0.891006
set ay2 to 0.453990
elseif ( angle_temp == 63 )
set ax1 to 0.891006
set ay1 to 0.453990
set ax2 to 0.898794
set ay2 to 0.438371
elseif ( angle_temp == 64 )
set ax1 to 0.898794
set ay1 to 0.438371
set ax2 to 0.906307
set ay2 to 0.422618
elseif ( angle_temp == 65 )
set ax1 to 0.906307
set ay1 to 0.422618
set ax2 to 0.913545
set ay2 to 0.406736
elseif ( angle_temp == 66 )
set ax1 to 0.913545
set ay1 to 0.406736
set ax2 to 0.920504
set ay2 to 0.390731
elseif ( angle_temp == 67 )
set ax1 to 0.920504
set ay1 to 0.390731
set ax2 to 0.927183
set ay2 to 0.374606
elseif ( angle_temp == 68 )
set ax1 to 0.927183
set ay1 to 0.374606
set ax2 to 0.933580
set ay2 to 0.358367
elseif ( angle_temp == 69 )
set ax1 to 0.933580
set ay1 to 0.358367
set ax2 to 0.939692
set ay2 to 0.342020
elseif ( angle_temp == 70 )
set ax1 to 0.939692
set ay1 to 0.342020
set ax2 to 0.945518
set ay2 to 0.325568
endif
elseif ( angle_temp <= 80 )
if ( angle_temp == 71 )
set ax1 to 0.945518
set ay1 to 0.325568
set ax2 to 0.951056
set ay2 to 0.309016
elseif ( angle_temp == 72 )
set ax1 to 0.951056
set ay1 to 0.309016
set ax2 to 0.956304
set ay2 to 0.292371
elseif ( angle_temp == 73 )
set ax1 to 0.956304
set ay1 to 0.292371
set ax2 to 0.961261
set ay2 to 0.275637
elseif ( angle_temp == 74 )
set ax1 to 0.961261
set ay1 to 0.275637
set ax2 to 0.965925
set ay2 to 0.258819
elseif ( angle_temp == 75 )
set ax1 to 0.965925
set ay1 to 0.258819
set ax2 to 0.970295
set ay2 to 0.241921
elseif ( angle_temp == 76 )
set ax1 to 0.970295
set ay1 to 0.241921
set ax2 to 0.974370
set ay2 to 0.224951
elseif ( angle_temp == 77 )
set ax1 to 0.974370
set ay1 to 0.224951
set ax2 to 0.978147
set ay2 to 0.207911
elseif ( angle_temp == 78 )
set ax1 to 0.978147
set ay1 to 0.207911
set ax2 to 0.981627
set ay2 to 0.190808
elseif ( angle_temp == 79 )
set ax1 to 0.981627
set ay1 to 0.190808
set ax2 to 0.984807
set ay2 to 0.173648
elseif ( angle_temp == 80 )
set ax1 to 0.984807
set ay1 to 0.173648
set ax2 to 0.987688
set ay2 to 0.156434
endif
elseif ( angle_temp <= 90 )
if ( angle_temp == 81 )
set ax1 to 0.987688
set ay1 to 0.156434
set ax2 to 0.990268
set ay2 to 0.139173
elseif ( angle_temp == 82 )
set ax1 to 0.990268
set ay1 to 0.139173
set ax2 to 0.992546
set ay2 to 0.121869
elseif ( angle_temp == 83 )
set ax1 to 0.992546
set ay1 to 0.121869
set ax2 to 0.994521
set ay2 to 0.104528
elseif ( angle_temp == 84 )
set ax1 to 0.994521
set ay1 to 0.104528
set ax2 to 0.996194
set ay2 to 0.087155
elseif ( angle_temp == 85 )
set ax1 to 0.996194
set ay1 to 0.087155
set ax2 to 0.997564
set ay2 to 0.069756
elseif ( angle_temp == 86 )
set ax1 to 0.997564
set ay1 to 0.069756
set ax2 to 0.998629
set ay2 to 0.052335
elseif ( angle_temp == 87 )
set ax1 to 0.998629
set ay1 to 0.052335
set ax2 to 0.999390
set ay2 to 0.034899
elseif ( angle_temp == 88 )
set ax1 to 0.999390
set ay1 to 0.034899
set ax2 to 0.999847
set ay2 to 0.017452
elseif ( angle_temp == 89 )
set ax1 to 0.999847
set ay1 to 0.017452
set ax2 to 1.000000
set ay2 to 0.000000
elseif ( angle_temp == 90 )
set ax1 to 1.000000
set ay1 to 0.000000
set ax2 to 0.999847
set ay2 to 0.017452
endif
endif
;Use simple linear extrapolation to approximate a decimal value for sine and cosine:
set angconvx1 to ( ax2 - ax1 ) ; calculate distance sin(angle) and sin(angle+1)
set angconvy1 to ( ay2 - ay1 ) ; same for cos
set angconvx2 to ( angconvx1 * angledec ) ;calculate a fraction by the decimal residue
set angconvy2 to ( angconvy1 * angledec ) ; same for cos
set axfinal to ( ax1 + angconvx2 ) ; set final result to result + fraction
set ayfinal to ( ay1 + angconvy2 ) ; set final result to result + fraction
;correct for quadrant:
if ( anglequad == 1 )
set axfinal to ( axfinal * 1 ) ; holds final sine
set ayfinal to ( ayfinal * 1 ) ; holds final cosine
elseif ( anglequad == 2 )
set axfinal to ( axfinal * 1 ) ; holds final sine
set ayfinal to ( ayfinal * -1 ) ; holds final cosine
elseif ( anglequad == 3 )
set axfinal to ( axfinal * -1 ) ; holds final sine
set ayfinal to ( ayfinal * -1 ) ; holds final cosine
elseif ( anglequad == 4 )
set axfinal to ( axfinal * -1 ) ; holds final sine
set ayfinal to ( ayfinal * 1 ) ; holds final cosine
endif
endwhile ; loop for all three axis
;-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
end jdtrigscript
