X-Git-Url: http://gitweb.hachti.de/?a=blobdiff_plain;f=lib%2Fhachti%2Fsrc%2Fmatrix.asm;h=79202db70cfda21765c874647f29d132b434d348;hb=c0fc7e111cb540730e471bc795309f65cf32a512;hp=34c42fb9903b7148e2ee050293c000e84c359d86;hpb=13f9c770845e6d9d77cc779c0d86cea366e721d0;p=h316.git

diff --git a/lib/hachti/src/matrix.asm b/lib/hachti/src/matrix.asm
index 34c42fb..79202db 100644
--- a/lib/hachti/src/matrix.asm
+++ b/lib/hachti/src/matrix.asm
@@ -91,7 +91,7 @@
 *                    M= |          |
 *                       | 0.0  1.0 |
 * 
-* WICH RESULTS TO THE IDENTITY TRANSFORMATION.
+* WHICH RESULTS TO THE IDENTITY TRANSFORMATION.
 * 
 *               JST     M$INIT
 *               DAC     MATRIX  POINTER TO A MATRIX
@@ -112,24 +112,29 @@
 * 
 * THIS ROUTINE CONVERTS THE VECTOR ELEMENTS TO FLOATING POINT VALUES,
 * APPLIES THE TRANSFORMATION TO THEM AND ROUNDS THE RESULTS BACK TO
-* INTEGER VALUES. THEN IT  SAVES THE NEW VECTOR IN THE PLACE OF THE 
-* OLD VECTOR.
+* INTEGER VALUES. THEN IT  SAVES THE NEW VECTOR TO THE LOCATION 
+* DESIGNATED BY THE TARGET ADDRESS. SOURCE AND TARGET MAY BE THE SAME,
+* THE SOURCE'S CONTENTS ARE NOT ALTERED.
 *
 *               JST     M$APLI
 *               DAC     MATRIX  MATRIX TO APPLY
-*               DAC     VECTOR  VECTOR TO TRANSFORM
+*               DAC     TARGET  POINTER TO TARGET VECTOR
+*               DAC     SOURCE  VECTOR TO TRANSFORM
 *               DAC     0       FOR FORTRAN IV COMPATIBILITY
 * 
 * 
 * M$APII: APPLY MATRIX TO PAIR OF INTEGERS AS VECTOR
 * 
-* THIS ROUTINE USES TWO DISTINCT INTEGER POINTERS INSTEAD OF ONE VECTOR
-* POINTER. THE REST OF THE BEHAVIOR IS EXACTLY LIKE M$APL.
+* THIS ROUTINE USES TWO DISTINCT INTEGER POINTERS TO DESCRIBE A POINT.
+* THE REST OF THE BEHAVIOR IS EXACTLY LIKE M$APL.
 * 
-*               JST     M$APLI
+*               JST     M$APII
 *               DAC     MATRIX  MATRIX TO APPLY
-*               DAC     X       X COORDINATE OF ARGUMENT VECTOR
-*               DAC     Y       Y COORDINATE OF ARGUMENT VECTOR
+*               DAC     XO      X COORDINATE OF RESULT VECTOR
+*               DAC     XO      Y COORDINATE OF RESULT VECTOR
+*               DAC     XI      X COORDINATE OF ARGUMENT VECTOR
+*               DAC     YI      Y COORDINATE OF ARGUMENT VECTOR
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY
 * 
 * 
 * M$ROT: ROTATE MATRIX
@@ -144,6 +149,17 @@
 *               JST     M$ROT
 *               DAC     MATRIX  MATRIX TO MODIFY
 *               DAC     ANGLE   RADIANT ANGLE
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY 
+* 
+* 
+* M$ROTI: ROTATE MATRIX
+* 
+* WORKS LIKE M$ROT, BUT TAKES AN INTEGER DEGREE VALUE AS ARGUMENT.
+*  
+*               JST     M$ROTI
+*               DAC     MATRIX  MATRIX TO MODIFY
+*               DAC     ANGLE   DEGREE ANGLE
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY 
 * 
 * 
 * M$SCLE: SCALE MATRIX
@@ -154,8 +170,89 @@
 *               JST     M$SCLE
 *               DAC     MATRIX  MATRIX TO MODIFY
 *               DAC     SCALE   SCALE FACTOR
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY 
+* 
+* 
+*********************************************************************************
+* 
+* 
+* T$INIT: INITIALISE AFFINE TRANSFORM
+*               
+*               JST     T$INIT
+*               DAC     TRANS   POINTER TO AFFINE TRANSFORMATION (SEE ABOVE)
+* 
+* 
+* T$SCLE: SCALE AFFINE TRANSFORMATION
+*               
+* THIS SCALES THE MATRIX OF THE AFFINE TRANSFORMATION BY FACTOR SCALE.
+* CALLS M$SCLE INTERNALLY.
+* 
+*               JST     T$SCLE
+*               DAC     TRANS   TRANSFORMATION TO MODIFY
+*               DAC     SCALE   SCALE FACTOR
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY 
+* 
+*  
+* T$TRAN: ADD RELOCATION TO AFFINE TRANSFORMATION
+* 
+* THE OFFSET VECTOR IS FIRST PROCESSED BY THE TRANSFORMATION.
+* THEN IT IS ADDED TO THE TRANSFORMATION'S TRANSLATION VECTOR.
+* 
+*               JST     T$TRAN
+*               DAC     TRANS   TRANSFORMATION TO MODIFY   
+*               DAC     XOFF    X OFFSET
+*               DAC     YOFF    Y OFFSET
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY 
+* 
+* 
+* T$ROT: ADD ROTATION TO AFFINE TRANSFORMATION
+* 
+* ADDS ROTATION TO THE MATRIX OF THE AFFINE TRANSFORMATION.
+* CALLS M$$ROT INTERNALLY.
+* 
+*               JST     T$ROT
+*               DAC     TRANS   TRANSFORMATION TO MODIFY
+*               DAC     ANGLE   ANGLE LIKE FOR M$ROT
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY
+* 
 * 
-*                
+* T$ROTI: ADD ROTATION TO AFFINE TRANSFORMATION
+* USES AN INTEGER ARGUMENT INSTEAD OF FLOATING POINT RADIANT.
+* 
+* ADDS ROTATION TO THE MATRIX OF THE AFFINE TRANSFORMATION.
+* CALLS M$$ROTI INTERNALLY.
+* 
+*               JST     T$ROTI
+*               DAC     TRANS   TRANSFORMATION TO MODIFY
+*               DAC     ANGLE   ANGLE LIKE FOR M$ROTI
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY
+* 
+* 
+* T$APII: APPLY AFFINE TRANSFORM TO PAIR OF INTEGERS AS VECTOR
+* 
+* WORKS LIKE M$APII WHICH IS USED INTERNALLY.
+*       
+*               JST     T$APII
+*               DAC     TRANS	TRANSFORMATION TO USE
+*               DAC     XO      X COORDINATE OF RESULT VECTOR
+*               DAC     XO      Y COORDINATE OF RESULT VECTOR
+*               DAC     XI      X COORDINATE OF ARGUMENT VECTOR
+*               DAC     YI      Y COORDINATE OF ARGUMENT VECTOR
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY
+*
+* 
+* T$APLI: APPLY AFFINE TRANSFORM TO VECTOR
+* 
+* WORKS LIKE M$APL WHICH IS USED INTERNALLY.
+* 
+*               JST     T$APLI
+*               DAC     TRANS
+*               DAC     TARGET  POINTER TO TARGET VECTOR
+*               DAC     SOURCE  POINTER TO INPUT VECTOR
+*               DAC     0       FOR FORTRAN IV COMPATIBILITY
+* 
+* 
+*                   
 ********************************************************************************
 *
 **** EXPORTED SYMBOLS
@@ -166,10 +263,19 @@
 	SUBR	M$APLI,APLI	APPLY MATRIX TO INTEGER VECTOR
 	SUBR	M$APII,APII	APPLY MATRIX TO PAIR OF INTEGERS
 	SUBR	M$ROT,ROT	ADD ROTATION TO MATRIX
+	SUBR	M$ROTI,ROTI	ADD ROTATION TO MATRIX
 	SUBR	M$SCLE,SCLE	SCALE MATRIX
+	SUBR	M$SCLI,SCLI	SCALE MATRIX (INTEGER PERCENT)
 *
-	SUBR	A$INIT,AFIN	INITIALISE AFFINE TRANSFORMATION
-* 
+	SUBR	T$INIT,AFIN	INITIALISE AFFINE TRANSFORMATION
+	SUBR	T$APLI,TPLI	APPLY AFFINE TRANSFORM TO INTEGER VECTOR
+	SUBR	T$APII,TPII	APPLY AFFINE TRANSFORM TO PAIR OF INTEGERS
+	SUBR	T$ROT,ROT	ADD ROTATION TO AFFINE TRANSFORMATION
+	SUBR	T$ROTI,ROTI	ADD ROTATION TO AFFINE TRANSFORMATION
+	SUBR	T$SCLE,SCLE	SCALE AFFINE TRANSFORMATION
+	SUBR	T$SCLI,SCLI	SCALE AFFINE TRANSFORMATION (INTEGER PERCENT)
+	SUBR	T$TRAN,TRAN	ADD TRANSLATION TO AFFINE TRANSFORMATION
+*  
 *  
 ********************************************************************************
 * 
@@ -178,7 +284,148 @@
 * 
 * 
 ********************************************************************************
-*
+* 
+* 
+*** T$TRAN - TRANSLATE
+* 
+* 
+*	ABS
+*	ORG	'4000
+TRAN	DAC	**	ENTRY.
+	LDA*	TRAN	TRANSFORMATION POINTER
+	STA	TPT
+	ADD	=8
+	STA	VECP
+	IRS	TRAN
+* 
+	LDA*	TRAN	X OFFSET
+	STA	XOFP
+	IRS	TRAN	
+* 
+	LDA*	TRAN	Y OFFSET
+	STA	YOFP
+	IRS	TRAN
+* 
+	IRS	TRAN	FOR FORTRAN IV
+* 
+	JST	APII	FIXME!
+TPT	DAC	**
+	DAC	TMP3	STORE NEW X VALUE IN TMP3
+	DAC	TMP4	STORE NEW Y VALUE IN TMP4
+XOFP	DAC	**
+YOFP	DAC	**
+	DAC	0	FOR FORTRAN IV COMPATIBILITY
+* 
+	LDA*	VECP
+	ADD	TMP3
+	STA*	VECP
+	IRS	VECP
+	LDA*	VECP
+	ADD	TMP4
+	STA*	VECP
+* 
+	JMP*	TRAN	RETURN.
+* 
+* 
+********************************************************************************
+* 
+* 
+**** T$APLI - APPLY AFFINE TRANSFORMATION TO INTEGER VECTOR
+* 
+* USED VARIABLES: ((TMP1) XOP,YOP,XP1,YP1,XP2,YP2),VECP
+* 
+TPLI	DAC	**	ENTRY.
+* 
+	LDA*	TPLI	LOAD POINTER TO TRANSFORMATION
+	STA	MPT	STORE TO MATRIX POINTER
+	ADD	=8	FORWARD TO VECTOR ADDRESS IN TRANSFORMATION
+	STA	VECP	VECTOR ADDRESS
+	IRS	TPLI
+*  
+	LDA*	TPLI	POINTER TO RESULT VECTOR
+	STA	IOV
+	IRS	TPLI
+* 
+	LDA*	TPLI	POINTER TO INPUT VECTOR
+	STA	IIV
+	IRS	TPLI
+* 
+	IRS	TPLI
+*  
+	JST	APLI	APPLY MATRIX
+MPT	DAC	**
+IOV	DAC	**
+IIV	DAC	**
+* 
+	LDA*	IOV	PERFORM VECTOR ADDITION
+	ADD*	VECP
+	STA*	IOV
+	IRS	VECP
+	IRS	IOV
+	LDA*	IOV
+	ADD*	VECP
+	STA*	IOV
+* 
+	JMP*	TPLI
+* 
+* 
+********************************************************************************
+* 
+* 
+**** T$APII - APPLY AFFINE TRANSFORMATION TO PAIR OF INTEGERS
+* 
+* USED VARIABLES: ((TMP1) XOP,YOP,XP1,YP1,XP2,YP2),VECP
+* 
+* 
+****************************************
+* 
+TPII	DAC	**	ENTRY.
+* 
+	LDA*	TPII	LOAD POINTER TO TRANSFORMATION
+	STA	IMPT	STORE TO MATRIX POINTER
+	ADD	=8	FORWARD TO VECTOR ADDRESS IN TRANSFORMATION
+	STA	VECP	VECTOR ADDRESS
+	IRS	TPII
+*  
+	LDA*	TPII	POINTER TO RESULT X
+	STA	RXP
+	IRS	TPII
+* 
+	LDA*	TPII	POINTER TO RESULT Y
+	STA	RYP
+	IRS	TPII
+* 
+	LDA*	TPII	POINTER TO INPUT X
+	STA	IXP
+	IRS	TPII
+* 
+	LDA*	TPII	POINTER TO INPUT Y
+	STA	IYP
+	IRS	TPII
+* 
+	IRS	TPII
+*  
+	JST	APII	APPLY MATRIX
+IMPT	DAC	**
+RXP	DAC	**	
+RYP	DAC	**
+IXP	DAC	**
+IYP	DAC	**
+	DAC	0
+* 
+	LDA*	VECP	PERFORM THE ADDITION
+	ADD*	RXP
+	STA*	RXP
+	IRS	VECP
+	LDA*	VECP
+	ADD*	RYP
+	STA*	RYP
+* 
+	JMP*	TPII	RETURN
+* 
+* 
+********************************************************************************
+* 
 * 
 **** INITIALIZE AFFINE TRANSFORMATION
 * 
@@ -210,24 +457,20 @@ AFI1	DAC	**
 * 
 INIT	DAC	**
 	LDX*	INIT	LOAD INDEX REGISTER WITH ADDRESS OF MATRIX
-	LDA*	INIT	LOAD MATRIX ADDRESS
-	STA	IM11	STORE POINTER TO FIRST ELEMENT (A11)
-	ADD	=6	IM12,IM21 ARE NOT TO BE INITIALISED WITH FP DATA
-	STA	IM22	STORE POINTER TO FOURTH ELEMENT (A22)
 	IRS	INIT	CORRECT RETURN ADDRESS
 *
 	CRA		INITIALISE
+	STA	1,1	A11, LOWER BITS
 	STA	2,1	A12
 	STA	3,1	          
 	STA	4,1	A21
-	STA	5,1	
-	CALL	FLOAT	GENERATE FLOATING POINT 1.0
-	DAC	ONE	CONSTANT INTEGER 1
-	CALL	H$22	STORE FLOATING POINT	
-IM11	DEC	0
-	CALL	H$22
-IM22	DEC	0
-*
+	STA	5,1
+	STA	7,1	A22, LOWER BITS	
+* 
+	LDA	ONEF	FLOATING POINT 1.0 CONSTANT
+	STA	0,1	A11, UPPER BITS
+	STA	6,1	A22, UPPER BITS
+* 
 	JMP*	INIT	RETURN.
 * 
 * 
@@ -333,33 +576,55 @@ PC22	DEC	0
 **** SCALE MATRIX
 * 
 SCLE	DAC	**	SCALE MATRIX
-	LDX*	SCLE
 *	
 	LDA*	SCLE	GET MATRIX BASE ADDRESS
 	STA	SM11
 	STA	TM11
-	ADD	=6
+	ADD	=2
+	STA	SM12
+	STA	TM12
+	ADD	=2
+	STA	SM21
+	STA	TM21
+	ADD	=2
 	STA	SM22
 	STA	TM22
 	IRS	SCLE
 	LDA*	SCLE
-	STA	SX
-	STA	SY
+	STA	S1
+	STA	S2
+	STA	S3
+	STA	S4
 	IRS	SCLE	TALLY RETURN ADDRESS
+	IRS	SCLE	AGAIN
 *
 	CALL	L$22
-SM11	DAC	0
+SM11	DAC	**
 	CALL	M$22
-SX	DAC	0
+S1	DAC	**
 	CALL	H$22
-TM11	DAC	0
+TM11	DAC	**
 *
 	CALL	L$22
-SM22	DAC	0
+SM12	DAC	**
 	CALL	M$22
-SY	DAC	0
+S2	DAC	**
 	CALL	H$22
-TM22	DAC	0
+TM12	DAC	**
+*
+	CALL	L$22
+SM21	DAC	**
+	CALL	M$22
+S3	DAC	**
+	CALL	H$22
+TM21	DAC	**
+*
+	CALL	L$22
+SM22	DAC	**
+	CALL	M$22
+S4	DAC	**
+	CALL	H$22
+TM22	DAC	**
 *
 	JMP*	SCLE
 *
@@ -367,17 +632,165 @@ TM22	DAC	0
 ********************************************************************************
 * 
 * 
-**** ROTATE MATRIX
+**** ADD ROTATION TO MATRIX
+*
+*  
+*    M =      M      *          MROT
 * 
-*       THIS ROUTINE IS NOT YET FINISHED!
+*        | M11 M12 |   | COS(X)  -SIN(X)|
+*      = |         | * |                |
+*        | M21 M22 |   | SIN( X)  COS(X)|
+* 
+*        | M11*COS(X)+M12*SIN(X)  M12*COS(X)-M11*SIN(X) |
+*      = |                                              |
+*        | M21*COS(X)+M22*SIN(X)  M22*COS(X)-M21*SIN(X) |
+* 
+* CALL:
+*       JST     ROT
+*       DAC     MATRIX
+*       DAC     ANGLE
+*       DAC     0       DON'T FORGET!
 * 
 ****************************************
 * 
 ROT	DAC	**	ENTRY
-	IRS	ROT	TALLY RETURN ADDRESS
-	JMP*	ROT	EXIT
 * 
+	LDA*	ROT	GET MATRIX POINTER
+	STA	R111	M11, FIRST COPY
+	STA	R211	M11, SECOND COPY
+	STA	R311	M11, THIRD COPY
+	ADD	=2
+	STA	R112
+	STA	R212
+	STA	R312
+	STA	R412
+	ADD	=2
+	STA	R121
+	STA	R221
+	STA	R321
+	ADD	=2
+	STA	R122
+	STA	R222
+	STA	R322
+	IRS	ROT
+	LDA*	ROT
+	STA	RA1
+	STA	RA2
+	IRS	ROT
+	IRS	ROT
+* 
+* 
+**** M11 CALCULATION
+* 
+	CALL	SIN	FLOATING POINT SINE
+RA1	DAC	**	POINTER TO ANGLE
+	CALL	H$22	SAVE TO TMP1
+	DAC	TMP1
+*	CALL	L$22
+*	DAC	TMP1
+	CALL	M$22	MULTIPLY
+R112	DAC	**	M12
+	CALL	H$22	STORE TO TMP3
+	DAC	TMP3
+* 
+*************************************
+* 
+	CALL	COS	FLOATING POINT COSINE
+RA2	DAC	**	POINTER TO ANGLE	
+	CALL	H$22	SAVE TO TMP2
+	DAC	TMP2
+	CALL	M$22	MULTIPLY
+R111	DAC	**	M11
+	CALL	A$22	ADD TMP3
+	DAC	TMP3
+	CALL	H$22	SAVE NEW M11 TO TMP3
+	DAC	TMP3
 * 
+* 
+* M12 CALCULATION
+* 
+* M12 = M12*COS(X)-M11*SIN(X)
+* 
+*  
+	CALL	L$22	LOAD SINE
+	DAC	TMP1
+	CALL	M$22	MULTIPLY
+R211	DAC	**	M11
+	CALL	H$22	STORE TO TMP4
+	DAC	TMP4
+	CALL	L$22	LOAD COSINE
+	DAC	TMP2
+	CALL	M$22	MULTIPLY
+R212	DAC	**
+* 
+	CALL	S$22	SUBSTRACT !!
+	DAC	TMP4
+* 
+	CALL	H$22	SAVE TO NEW M12
+R312	DAC	**
+*
+ 	CALL	L$22	LOAD NEW M11 FROM TMP3
+	DAC	TMP3
+	CALL	H$22	AND SAVE TO NEW M11
+R311	DAC	**
+* 
+* 
+* ******************************************
+* 
+* M21 CALCULATION
+* 
+* M21*COS(X)+M22*SIN(X)
+* 
+* M22*SIN(X) -> TMP3
+* M21*COS(X) - TMP3
+* 
+* 
+*    
+	CALL	L$22	LOAD SINE
+	DAC	TMP1
+	CALL	M$22	MULTIPLY
+R122	DAC	**	M22
+	CALL	H$22	STORE TO TMP3
+	DAC	TMP3
+	CALL	L$22	LOAD COSINE
+	DAC	TMP2
+	CALL	M$22	MULTIPLY
+R121	DAC	**	M11
+	CALL	A$22	ADD TMP3
+	DAC	TMP3
+	CALL	H$22	SAVE NEW M21 TO TMP3
+	DAC	TMP3
+*
+* M22 CALCULATION
+* 
+* M22*COS(X)-M21*SIN(X)
+* 
+* 
+* 	JMP	NN	
+	CALL	L$22	LOAD SINE
+	DAC	TMP1
+	CALL	M$22	MULTIPLY
+R221	DAC	**	M21
+	CALL	H$22	STORE TO TMP4
+	DAC	TMP4
+	CALL	L$22	LOAD COSINE
+	DAC	TMP2
+	CALL	M$22	MULTIPLY
+R222	DAC	**
+	CALL	S$22	SUBSTRACT
+	DAC	TMP4
+	CALL	H$22	SAVE TO NEW M22
+R322	DAC	**
+	CALL	L$22	LOAD NEW M21 FROM TMP3
+	DAC	TMP3
+	CALL	H$22	AND SAVE TO NEW M21
+R321	DAC	**
+* 
+*        
+	JMP*	ROT	RETURN.
+*
+R412	DAC	**
+*  
 ********************************************************************************
 *
 *
@@ -389,33 +802,45 @@ ROT	DAC	**	ENTRY
 * CALL:
 *       JST     M$APII
 *       DAC     MATRIX
-*       DAC     X	
-*       DAC     Y
+*       DAC     XO	
+*       DAC     YO
+*       DAC     XI	
+*       DAC     YI
 *       DAC     0       DON'T FORGET!
 * 
+* USED VARIABLES: (TMP1) XOP,YOP,XP1,YP1,XP2,YP2
+* 
 ****************************************
 *
 APII	DAC	**
 *
-	LDA*	APII
-	STA	MP11
-	ADD	=2
-	STA	MP12
-	ADD	=2
-	STA	MP21
-	ADD	=2
-	STA	MP22
-	IRS	APII
-*
-	LDA*	APII
-	STA	XP1
-	STA	XP2
-	IRS	APII
-	LDA*	APII
-	STA	YP1
-	STA	YP2
-	IRS	APII
-	IRS	APII
+	LDA*	APII	POINTER TO MATRIX
+	STA	MP11	STORE M11
+	ADD	=2	ADD 2
+	STA	MP12	STORE M12
+	ADD	=2	ADD 2
+	STA	MP21	STORE M21
+	ADD	=2	ADD 2
+	STA	MP22	STORE M22
+	IRS	APII	JUMP TO NEXT ARGUMENT (X)
+*
+	LDA*	APII	LOAD X VALUE
+	STA	XOP	STORE TO X-POINTER
+	IRS	APII	JUMP TO NEXT ARGUMENT (Y)
+	LDA*	APII	LOAD Y VALUE
+	STA	YOP	STORE TO Y-POINTER
+	IRS	APII	CORRECT RETURN ADDRESS
+* 
+	LDA*	APII	LOAD X VALUE
+	STA	XIP1	STORE TO X-POINTER
+	STA	XIP2	STORE TO X-POINTER
+	IRS	APII	JUMP TO NEXT ARGUMENT (Y)
+	LDA*	APII	LOAD Y VALUE
+	STA	YIP1	STORE TO Y-POINTER
+	STA	YIP2	STORE TO Y-POINTER
+	IRS	APII	CORRECT RETURN ADDRESS
+* 
+	IRS	APII	FOR FORTRANIV COMPATIBILITY
 	JST	APL	CALL REAL ROUTINE
 	JMP*	APII
 *	
@@ -430,9 +855,12 @@ APII	DAC	**
 * CALL:
 *       JST     M$APLI
 *       DAC     MATRIX
-*       DAC     VECTOR
+*       DAC	TARGET
+*       DAC     SOURCE
 *       DAC     0       DON'T FORGET!
 * 
+* USED VARIABLES: (TMP1) XOP,YOP,XP1,YP1,XP2,YP2
+* 
 ****************************************
 *
 APLI	DAC	**
@@ -448,12 +876,19 @@ APLI	DAC	**
 	IRS	APLI
 *
 	LDA*	APLI
-	STA	XP1
-	STA	XP2
+	STA	XOP
 	AOA
-	STA	YP1
-	STA	YP2
+	STA	YOP
 	IRS	APLI
+* 
+	LDA*	APLI
+	STA	XIP1
+	STA	XIP2
+	AOA
+	STA	YIP1
+	STA	YIP2
+	IRS	APLI
+* 
 	IRS	APLI
 	JST	APL	CALL INTERNAL ROUTINE
 	JMP*	APLI	RETURN.
@@ -466,47 +901,103 @@ APLI	DAC	**
 * 
 * ALL DATA IS SET UP BY THE BOTH USER ROUTINES ABOVE.
 * 
+* USED VARIABLES: TMP1
+* 
 ****************************************
 * 
 APL	DAC	**	
 *
 	CALL	FLOAT	LOAD SINGLE PRECISION FLOAT FROM 1-WORD INTEGER
-XP1	DAC	0
+XIP1	DAC	0
 	CALL	M$22	MULTIPLY FLOAT*FLOAT
 MP11	DAC	0
 	CALL	H$22	STORE FLOAT
-	DAC	TMP
+	DAC	TMP1
 	CALL	FLOAT
-YP1	DAC	0
+YIP1	DAC	0
 	CALL	M$22
 MP12	DAC	0
 	CALL	A$22
-	DAC	TMP
+	DAC	TMP1
 	JST	RND	ROUND AND CONVERT TO INTEGER
 	STA	PA21	STORE NEW X VALUE INTO TEMPORARY LOCATION
 ****
 	CALL	FLOAT
-XP2	DAC	0
+XIP2	DAC	0
 	CALL	M$22
 MP21	DAC	0
 	CALL	H$22
-	DAC	TMP
+	DAC	TMP1
 *
 	CALL	FLOAT
-YP2	DAC	0
+YIP2	DAC	0
 	CALL	M$22
 MP22	DAC	0
 	CALL	A$22
-	DAC	TMP
+	DAC	TMP1
 	JST	RND	NOW INTEGER IN AC
-	STA*	YP1	STORE NEW Y VALUE
+	STA*	YOP	STORE NEW Y VALUE
 *
 	LDA	PA21
-	STA*	XP1
+	STA*	XOP
+* 
 	JMP*	APL	RETURN TO CALLER.
 *
 * 
 ********************************************************************************
+* 
+* 
+**** M$ROTI ROTATE MATRIX, USE INTEGER DEGREE ANGLE
+* 
+ROTI	DAC	**
+	LDA*	ROTI	GET MATRIX POINTER
+	STA	MTA	STORE TO ARGUMENT TO FINAL ROT
+	IRS	ROTI	NEXT ARGUMENT: ANGLE
+	LDA*	ROTI	LOAD ANGLE
+	IRS	ROTI	
+	IRS	ROTI
+	JST	RAD	CONVERT INTEGER TO RADIANT
+	CALL	H$22
+	DAC	RTMP
+	JST	ROT
+MTA	DAC	**
+	DAC	RTMP
+	DAC	0	
+	JMP*	ROTI
+* 
+RTMP	BSS	2	TEMPORARY VARIABLE
+* 
+* 
+********************************************************************************
+* 
+* 
+**** M$SCLI - SCALE MATRIX, USE INTEGER PERCENT VALUE
+* 
+SCLI	DAC	**
+	LDA*	SCLI	GET MATRIX POINTER
+	STA	MTSS	STORE TO ARGUMENT TO FINAL ROT
+	IRS	SCLI	NEXT ARGUMENT: PERCENTS
+* 
+	LDA*	SCLI	LOAD PERCENTS
+	STA	SA1	STORE
+	CALL	FLOAT	CONVERT TO FLOAT
+SA1	DAC	**
+	CALL	M$22	MULTIPLY WITH
+	DAC	PERC	FACTOR 0.01
+	IRS	SCLI	
+	IRS	SCLI
+	CALL	H$22
+	DAC	RTMP
+* 
+	JST	SCLE
+MTSS	DAC	**
+  	DAC	RTMP
+	DAC	0
+* 
+	JMP*	SCLI	RETURN
+* 
+* 
+********************************************************************************
 *
 * 
 **** ROUND FLOAT TO INTEGER ROUTINE
@@ -529,19 +1020,57 @@ RND	DAC	**
 ********************************************************************************
 * 
 * 
+**** RAD - CONVERT ANGLE IN DEGREE TO RADIANT.
+* 
+* ENTER WITH INTEGER ANGLE IN A
+* 
+* CALL:
+* 
+*       JST     RAD
+*       DAC     ANGLE   POINTER TO ANGLE
+* 
+****************************************
+* 
+RAD	DAC	**
+	STA	AN1
+	CALL	FLOAT
+AN1	DAC	**
+	CALL	M$22
+	DAC	DEG
+	JMP*	RAD
+* 
+*  
+********************************************************************************
+* 
+* 
 **** CONSTANTS
 * 
 ONE	DEC	1
 HLF	OCT	'040100	CONSTANT 0.5	
 	OCT	'000000
+ONEF	OCT	'040300	CONSTANT 1.0
+	OCT	'000000
+DEG	OCT	'036707	CONSTANT PI/180
+	OCT	'076432
+PERC	OCT	'036521	CONTANT 0.01
+	OCT	'165605
 * 
 * 
 ********************************************************************************
 * 
+* 
 **** VARIABLES
 * 
-TMP	BSS	'10	SOME SPACE
-*
+TMP1	BSS	'2	TEMPORARY 2-WORD VARIABLE
+TMP2	BSS	'2	      "      "      "
+TMP3	BSS	'2	      "      "      "   
+TMP4	BSS	'2	      "      "      "
+VAP	DAC	**	TEMPORARY POINTER TO VECTOR
+XOP	DAC	**	OUTPUT VECTOR X POINTER
+YOP	DAC	**	OUTPUT VECTOR Y POINTER
+*VECP	DAC	**	VECTOR POINTER USED BY T$PII,T$PLI
+VECP	EQU	TMP2	VECTOR POINTER USED BY T$PII,T$PLI
+* 
 *
 ********************************************************************************
 *