/* $Xorg: spaces.c,v 1.4 2000/08/17 19:46:32 cpqbld Exp $ */ /* Copyright International Business Machines, Corp. 1991 * All Rights Reserved * Copyright Lexmark International, Inc. 1991 * All Rights Reserved * * License to use, copy, modify, and distribute this software and its * documentation for any purpose and without fee is hereby granted, * provided that the above copyright notice appear in all copies and that * both that copyright notice and this permission notice appear in * supporting documentation, and that the name of IBM or Lexmark not be * used in advertising or publicity pertaining to distribution of the * software without specific, written prior permission. * * IBM AND LEXMARK PROVIDE THIS SOFTWARE "AS IS", WITHOUT ANY WARRANTIES OF * ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO ANY * IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, * AND NONINFRINGEMENT OF THIRD PARTY RIGHTS. THE ENTIRE RISK AS TO THE * QUALITY AND PERFORMANCE OF THE SOFTWARE, INCLUDING ANY DUTY TO SUPPORT * OR MAINTAIN, BELONGS TO THE LICENSEE. SHOULD ANY PORTION OF THE * SOFTWARE PROVE DEFECTIVE, THE LICENSEE (NOT IBM OR LEXMARK) ASSUMES THE * ENTIRE COST OF ALL SERVICING, REPAIR AND CORRECTION. IN NO EVENT SHALL * IBM OR LEXMARK BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL * DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR * PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF * THIS SOFTWARE. */ /* $XFree86: xc/lib/font/Type1/spaces.c,v 3.11 2003/05/27 22:26:47 tsi Exp $ */ /* SPACES CWEB V0021 ******** */ /* :h1 id=spaces.SPACES Module - Handles Coordinate Spaces This module is responsible for handling the TYPE1IMAGER "XYspace" object. &author. Jeffrey B. Lotspiech (lotspiech@almaden.ibm.com) :h3.Include Files */ #ifdef FONTMODULE #include "Xdefs.h" /* Bool declaration ??? */ #include "Xmd.h" /* INT32 declaration ??? */ #include "os.h" #include "xf86_ansic.h" #else #include "X11/Xos.h" #include "os.h" #endif #include "objects.h" #include "spaces.h" #include "paths.h" #include "pictures.h" #include "fonts.h" #include "arith.h" #include "trig.h" static void FindFfcn ( double cx, double cy, convertFunc *fcnP ); static void FindIfcn ( double cx, double cy, fractpel *icxP, fractpel *icyP, iconvertFunc *fcnP ); /* :h3.Entry Points Provided to the TYPE1IMAGER User */ /*SHARED LINE(S) ORIGINATED HERE*/ /* :h3.Entry Points Provided to Other Modules */ /* In addition, other modules call the SPACES module through function vectors in the "XYspace" structure. The entry points accessed that way are "FConvert()", "IConvert()", and "ForceFloat()". */ /*SHARED LINE(S) ORIGINATED HERE*/ /* :h3.Macros and Typedefs Provided to Other Modules :h4.Duplicating and Killing Spaces Destroying XYspaces is so simple we can do it with a macro: */ /*SHARED LINE(S) ORIGINATED HERE*/ /* On the other hand, duplicating XYspaces is slightly more difficult because of the need to keep a unique ID in the space, see :hdref refid=dupspace.. :h4.Fixed Point Pel Representation We represent pel positions with fixed point numbers. This does NOT mean integer, but truly means fixed point, with a certain number of binary digits (FRACTBITS) representing the fractional part of the pel. */ /*SHARED LINE(S) ORIGINATED HERE*/ /* :h2.Data Structures for Coordinate Spaces and Points */ /* :h3 id=matrix.Matrices TYPE1IMAGER uses 2x2 transformation matrices. We'll use C notation for such a matrix (M[2][2]), the first index being rows, the second columns. */ /* :h3.The "doublematrix" Structure We frequently find it desirable to store both a matrix and its inverse. We store these in a "doublematrix" structure. */ /*SHARED LINE(S) ORIGINATED HERE*/ /* :h3.The "XYspace" Structure The XYspace structure represents the XYspace object. */ /*SHARED LINE(S) ORIGINATED HERE*/ #define RESERVED 10 /* 'n' IDs are reserved for invalid & immortal spaces */ /* */ #define NEXTID ((SpaceID < RESERVED) ? (SpaceID = RESERVED) : ++SpaceID) static unsigned int SpaceID = 1; struct XYspace * CopySpace(struct XYspace *S) { S = (struct XYspace *)Allocate(sizeof(struct XYspace), S, 0); S->ID = NEXTID; return(S); } /* :h3.The "fractpoint" Structure A fractional point is just a "fractpel" x and y: */ /*SHARED LINE(S) ORIGINATED HERE*/ /* :h3.Lazy Evaluation of Matrix Inverses Calculating the inverse of a matrix is somewhat involved, and we usually do not need them. So, we flag whether or not the space has the inverse already calculated: */ #define HASINVERSE(flag) ((flag)&0x80) /* The following macro forces a space to have an inverse: */ #define CoerceInverse(S) if (!HASINVERSE((S)->flag)) { \ MatrixInvert((S)->tofract.normal, (S)->tofract.inverse); (S)->flag |= HASINVERSE(ON); } /* :h3.IDENTITY Space IDENTITY space is (logically) the space corresponding to the identity transformation matrix. However, since all our transformation matrices have a common FRACTFLOAT scale factor to convert to 'fractpel's, that is actually what we store in 'tofract' matrix of IDENTITY: */ static struct XYspace identity = { SPACETYPE, ISPERMANENT(ON) + ISIMMORTAL(ON) + HASINVERSE(ON), 2, /* added 3-26-91 PNM */ NULL, NULL, NULL, NULL, NULL, NULL, INVALIDID + 1, 0, {{{FRACTFLOAT, 0.0}, {0.0, FRACTFLOAT}}, {{1.0/FRACTFLOAT, 0.0}, {0.0, 1.0/FRACTFLOAT}}}, {{0, 0}, {0, 0}}}; struct XYspace *IDENTITY = &identity; /* */ #define MAXCONTEXTS 16 static struct doublematrix contexts[MAXCONTEXTS]; #ifdef notdef static int nextcontext = 1; /*SHARED LINE(S) ORIGINATED HERE*/ /* :h3.FindDeviceContext() - Find the Context Given a Device This routine, given a device, returns the index of the device's transformation matrix in the context array. If it cannot find it, it will allocate a new array entry and fill it out. */ static int FindDeviceContext(pointer device) /* device token */ { double M[2][2]; /* temporary matrix */ float Xres,Yres; /* device resolution */ int orient = -1; /* device orientation */ int rc = -1; /* return code for QueryDeviceState */ if (rc != 0) /* we only bother with this check once */ Abort("Context: QueryDeviceState didn't work"); M[0][0] = M[1][0] = M[0][1] = M[1][1] = 0.0; switch (orient) { case 0: M[0][0] = Xres; M[1][1] = -Yres; break; case 1: M[1][0] = Yres; M[0][1] = Xres; break; case 2: M[0][0] = -Xres; M[1][1] = Yres; break; case 3: M[1][0] = -Yres; M[0][1] = -Xres; break; default: Abort("QueryDeviceState returned invalid orientation"); } return(FindContext(M)); } /* :h3.FindContext() - Find the Context Given a Matrix This routine, given a matrix, returns the index of that matrix matrix in the context array. If it cannot find it, it will allocate a new array entry and fill it out. */ int FindContext(double M[2][2]) /* array to search for */ { register int i; /* loop variable for search */ for (i=0; i < nextcontext; i++) if (M[0][0] == contexts[i].normal[0][0] && M[1][0] == contexts[i].normal[1][0] && M[0][1] == contexts[i].normal[0][1] && M[1][1] == contexts[i].normal[1][1]) break; if (i >= nextcontext) { if (i >= MAXCONTEXTS) Abort("Context: out of them"); LONGCOPY(contexts[i].normal, M, sizeof(contexts[i].normal)); MatrixInvert(M, contexts[i].inverse); nextcontext++; } return(i); } /* :h3.Context() - Create a Coordinate Space for a Device This user operator is implemented by first finding the device context array index, then transforming IDENTITY space to create an appropriate cooridnate space. */ struct XYspace * Context(pointer device, /* device token */ double units) /* multiples of one inch */ { double M[2][2]; /* device transformation matrix */ register int n; /* will hold device context number */ register struct XYspace *S; /* XYspace constructed */ ARGCHECK((device == NULL), "Context of NULLDEVICE not allowed", NULL, IDENTITY, (0), struct XYspace *); ARGCHECK((units == 0.0), "Context: bad units", NULL, IDENTITY, (0), struct XYspace *); n = FindDeviceContext(device); LONGCOPY(M, contexts[n].normal, sizeof(M)); M[0][0] *= units; M[0][1] *= units; M[1][0] *= units; M[1][1] *= units; S = (struct XYspace *)Xform(IDENTITY, M); S->context = n; return(S); } #endif /* :h3.ConsiderContext() - Adjust a Matrix to Take Out Device Transform Remember, we have :f/x times U times D/ and :f/M/ and and we want :f/x times U times M times D/. An easy way to do this is to calculate :f/D sup <-1> times M times D/, because: :formula. x times U times D times D sup <-1> times M times D = x times U times M times D :formula. So this subroutine, given an :f/M/and an object, finds the :f/D/ for that object and modifies :f/M/ so it is :f/D sup <-1> times M times D/. */ static void ConsiderContext(struct xobject *obj, /* object to be transformed */ double M[2][2]) /* matrix (may be changed) */ { register int context = 0; /* index in contexts array */ if (obj == NULL) return; if (ISPATHTYPE(obj->type)) { struct segment *path = (struct segment *) obj; context = path->context; } else if (obj->type == SPACETYPE) { struct XYspace *S = (struct XYspace *) obj; context = S->context; } else if (obj->type == PICTURETYPE) { } else context = NULLCONTEXT; if (context != NULLCONTEXT) { MatrixMultiply(contexts[context].inverse, M, M); MatrixMultiply(M, contexts[context].normal, M); } } /* :h2.Conversion from User's X,Y to "fractpel" X,Y When the user is building paths (lines, moves, curves, etc.) he passes the control points (x,y) for the paths together with an XYspace. We must convert from the user's (x,y) to our internal representation which is in pels (fractpels, actually). This involves transforming the user's (x,y) under the coordinate space transformation. It is important that we do this quickly. So, we store pointers to different conversion functions right in the XYspace structure. This allows us to have simpler special case functions for the more commonly encountered types of transformations. :h3.Convert(), IConvert(), and ForceFloat() - Called Through "XYspace" Structure These are functions that fit in the "convert" and "iconvert" function pointers in the XYspace structure. They call the "xconvert", "yconvert", "ixconvert", and "iyconvert" as appropriate to actually do the work. These secondary routines come in many flavors to handle different special cases as quickly as possible. */ static void FXYConvert(struct fractpoint *pt, /* point to set */ struct XYspace *S, /* relevant coordinate space */ double x, double y) /* user's coordinates of point */ { pt->x = (*S->xconvert)(S->tofract.normal[0][0], S->tofract.normal[1][0], x, y); pt->y = (*S->yconvert)(S->tofract.normal[0][1], S->tofract.normal[1][1], x, y); } static void IXYConvert(struct fractpoint *pt, /* point to set */ struct XYspace *S, /* relevant coordinate space */ long x, long y) /* user's coordinates of point */ { pt->x = (*S->ixconvert)(S->itofract[0][0], S->itofract[1][0], x, y); pt->y = (*S->iyconvert)(S->itofract[0][1], S->itofract[1][1], x, y); } /* ForceFloat is a substitute for IConvert(), when we just do not have enough significant digits in the coefficients to get high enough precision in the answer with fixed point arithmetic. So, we force the integers to floats, and do the arithmetic all with floats: */ static void ForceFloat(struct fractpoint *pt, /* point to set */ struct XYspace *S, /* relevant coordinate space */ long x, long y) /* user's coordinates of point */ { (*S->convert)(pt, S, (double) x, (double) y); } /* :h3.FXYboth(), FXonly(), FYonly() - Floating Point Conversion These are the routines we use when the user has given us floating point numbers for x and y. FXYboth() is the general purpose routine; FXonly() and FYonly() are special cases when one of the coefficients is 0.0. */ static fractpel FXYboth(double cx, double cy, /* x and y coefficients */ double x, double y) /* user x,y */ { register double r; /* temporary float */ r = x * cx + y * cy; return((fractpel) r); } /*ARGSUSED*/ static fractpel FXonly(double cx, double cy, /* x and y coefficients */ double x, double y) /* user x,y */ { register double r; /* temporary float */ r = x * cx; return((fractpel) r); } /*ARGSUSED*/ static fractpel FYonly(double cx, double cy, /* x and y coefficients */ double x, double y) /* user x,y */ { register double r; /* temporary float */ r = y * cy; return((fractpel) r); } /* :h3.IXYboth(), IXonly(), IYonly() - Simple Integer Conversion These are the routines we use when the user has given us integers for x and y, and the coefficients have enough significant digits to provide precise answers with only "long" (32 bit?) multiplication. IXYboth() is the general purpose routine; IXonly() and IYonly() are special cases when one of the coefficients is 0. */ static fractpel IXYboth(fractpel cx, fractpel cy, /* x and y coefficients */ long x, long y) /* user x,y */ { return(x * cx + y * cy); } /*ARGSUSED*/ static fractpel IXonly(fractpel cx, fractpel cy, /* x and y coefficients */ long x, long y) /* user x,y */ { return(x * cx); } /*ARGSUSED*/ static fractpel IYonly(fractpel cx, fractpel cy, /* x and y coefficients */ long x, long y) /* user x,y */ { return(y * cy); } /* :h3.FPXYboth(), FPXonly(), FPYonly() - More Involved Integer Conversion These are the routines we use when the user has given us integers for x and y, but the coefficients do not have enough significant digits to provide precise answers with only "long" (32 bit?) multiplication. We have increased the number of significant bits in the coefficients by FRACTBITS; therefore we must use "double long" (64 bit?) multiplication by calling FPmult(). FPXYboth() is the general purpose routine; FPXonly() and FPYonly() are special cases when one of the coefficients is 0. Note that it is perfectly possible for us to calculate X with the "FP" method and Y with the "I" method, or vice versa. It all depends on how the functions in the XYspace structure are filled out. */ static fractpel FPXYboth(fractpel cx, fractpel cy, /* x and y coefficients */ long x, long y) /* user x,y */ { return( FPmult(x, cx) + FPmult(y, cy) ); } /*ARGSUSED*/ static fractpel FPXonly(fractpel cx, fractpel cy, /* x and y coefficients */ long x, long y) /* user x,y */ { return( FPmult(x, cx) ); } /*ARGSUSED*/ static fractpel FPYonly(fractpel cx, fractpel cy, /* x and y coefficients */ long x, long y) /* user x,y */ { return( FPmult(y, cy) ); } /* :h3.FillOutFcns() - Determine the Appropriate Functions to Use for Conversion This function fills out the "convert" and "iconvert" function pointers in an XYspace structure, and also fills the "helper" functions that actually do the work. */ static void FillOutFcns(struct XYspace *S) /* functions will be set in this structure */ { S->convert = FXYConvert; S->iconvert = IXYConvert; FindFfcn(S->tofract.normal[0][0], S->tofract.normal[1][0], &S->xconvert); FindFfcn(S->tofract.normal[0][1], S->tofract.normal[1][1], &S->yconvert); FindIfcn(S->tofract.normal[0][0], S->tofract.normal[1][0], &S->itofract[0][0], &S->itofract[1][0], &S->ixconvert); FindIfcn(S->tofract.normal[0][1], S->tofract.normal[1][1], &S->itofract[0][1], &S->itofract[1][1], &S->iyconvert); if (S->ixconvert == NULL || S->iyconvert == NULL) S->iconvert = ForceFloat; } /* :h4.FindFfcn() - Subroutine of FillOutFcns() to Fill Out Floating Functions This function tests for the special case of one of the coefficients being zero: */ static void FindFfcn(double cx, double cy, /* x and y coefficients */ convertFunc *fcnP) /* pointer to function to set */ { if (cx == 0.0) *fcnP = FYonly; else if (cy == 0.0) *fcnP = FXonly; else *fcnP = FXYboth; } /* :h4.FindIfcn() - Subroutine of FillOutFcns() to Fill Out Integer Functions There are two types of integer functions, the 'I' type and the 'FP' type. We use the I type functions when we are satisfied with simple integer arithmetic. We used the FP functions when we feel we need higher precision (but still fixed point) arithmetic. If all else fails, we store a NULL indicating that this we should do the conversion in floating point. */ static void FindIfcn(double cx, double cy, /* x and y coefficients */ fractpel *icxP, fractpel *icyP, /* fixed point coefficients to set */ iconvertFunc *fcnP) /* pointer to function to set */ { register fractpel imax; /* maximum of cx and cy */ *icxP = cx; *icyP = cy; if (cx != (float) (*icxP) || cy != (float) (*icyP)) { /* At this point we know our integer approximations of the coefficients are not exact. However, we will still use them if the maximum coefficient will not fit in a 'fractpel'. Of course, we have little choice at that point, but we haven't lost that much precision by staying with integer arithmetic. We have enough significant digits so that any error we introduce is less than one part in 2:sup/16/. */ imax = MAX(ABS(*icxP), ABS(*icyP)); if (imax < (fractpel) (1<<(FRACTBITS-1)) ) { /* At this point we know our integer approximations just do not have enough significant digits for accuracy. We will add FRACTBITS significant digits to the coefficients (by multiplying them by 1<<FRACTBITS) and go to the "FP" form of the functions. First, we check to see if we have ANY significant digits at all (that is, if imax == 0). If we don't, we suspect that adding FRACTBITS digits won't help, so we punt the whole thing. */ if (imax == 0) { *fcnP = NULL; return; } cx *= FRACTFLOAT; cy *= FRACTFLOAT; *icxP = cx; *icyP = cy; *fcnP = FPXYboth; } else *fcnP = IXYboth; } else *fcnP = IXYboth; /* Now we check for special cases where one coefficient is zero (after integer conversion): */ if (*icxP == 0) *fcnP = (*fcnP == FPXYboth) ? FPYonly : IYonly; else if (*icyP == 0) *fcnP = (*fcnP == FPXYboth) ? FPXonly : IXonly; } /* :h3.UnConvert() - Find User Coordinates From FractPoints The interesting thing with this routine is that we avoid calculating the matrix inverse of the device transformation until we really need it, which is to say, until this routine is called for the first time with a given coordinate space. We also only calculate it only once. If the inverted matrix is valid, we don't calculate it; if not, we do. We never expect matrices with zero determinants, so by convention, we mark the matrix is invalid by marking both X terms zero. */ void UnConvert(struct XYspace *S, /* relevant coordinate space */ struct fractpoint *pt, /* device coordinates */ double *xp, double *yp) /* where to store resulting x,y */ { double x,y; CoerceInverse(S); x = pt->x; y = pt->y; *xp = S->tofract.inverse[0][0] * x + S->tofract.inverse[1][0] * y; *yp = S->tofract.inverse[0][1] * x + S->tofract.inverse[1][1] * y; } /* :h2.Transformations */ /* :h3 id=xform.Xform() - Transform Object in X and Y TYPE1IMAGER wants transformations of objects like paths to be identical to transformations of spaces. For example, if you scale a line(1,1) by 10 it should yield the same result as generating the line(1,1) in a coordinate space that has been scaled by 10. We handle fonts by storing the accumulated transform, for example, SR (accumulating on the right). Then when we map the font through space TD, for example, we multiply the accumulated font transform on the left by the space transform on the right, yielding SRTD in this case. We will get the same result if we did S, then R, then T on the space and mapping an unmodified font through that space. */ struct xobject * t1_Xform(struct xobject *obj, /* object to transform */ double M[2][2]) /* transformation matrix */ { if (obj == NULL) return(NULL); if (obj->type == FONTTYPE) { register struct font *F = (struct font *) obj; F = UniqueFont(F); return((struct xobject*)F); } if (obj->type == PICTURETYPE) { /* In the case of a picture, we choose both to update the picture's transformation matrix and keep the handles up to date. */ register struct picture *P = (struct picture *) obj; register struct segment *handles; /* temporary path to transform handles */ P = UniquePicture(P); handles = PathSegment(LINETYPE, P->origin.x, P->origin.y); handles = Join(handles, PathSegment(LINETYPE, P->ending.x, P->ending.y) ); handles = (struct segment *)Xform((struct xobject *) handles, M); P->origin = handles->dest; P->ending = handles->link->dest; KillPath(handles); return((struct xobject *)P); } if (ISPATHTYPE(obj->type)) { struct XYspace pseudo; /* local temporary space */ PseudoSpace(&pseudo, M); return((struct xobject *) PathTransform((struct segment *)obj, &pseudo)); } if (obj->type == SPACETYPE) { register struct XYspace *S = (struct XYspace *) obj; /* replaced ISPERMANENT(S->flag) with S->references > 1 3-26-91 PNM */ if (S->references > 1) S = CopySpace(S); else S->ID = NEXTID; MatrixMultiply(S->tofract.normal, M, S->tofract.normal); /* * mark inverted matrix invalid: */ S->flag &= ~HASINVERSE(ON); FillOutFcns(S); return((struct xobject *) S); } return(ArgErr("Untransformable object", obj, obj)); } /* :h3.Transform() - Transform an Object This is the external user's entry point. */ struct xobject * t1_Transform(struct xobject *obj, double cxx, double cyx, /* 2x2 transform matrix elements */ double cxy, double cyy) /* in row order */ { double M[2][2]; M[0][0] = cxx; M[0][1] = cyx; M[1][0] = cxy; M[1][1] = cyy; ConsiderContext(obj, M); return(Xform(obj, M)); } /* :h3.Scale() - Special Case of Transform() This is a user operator. */ struct xobject * t1_Scale(struct xobject *obj, /* object to scale */ double sx, double sy) /* scale factors in x and y */ { double M[2][2]; M[0][0] = sx; M[1][1] = sy; M[1][0] = M[0][1] = 0.0; ConsiderContext(obj, M); return(Xform(obj, M)); } /* :h3 id=rotate.Rotate() - Special Case of Transform() We special-case different settings of 'degrees' for performance and accuracy within the DegreeSin() and DegreeCos() routines themselves. */ #ifdef notdef struct xobject * xiRotate(struct xobject *obj, /* object to be transformed */ double degrees) /* degrees of COUNTER-clockwise rotation */ { double M[2][2]; M[0][0] = M[1][1] = DegreeCos(degrees); M[1][0] = - (M[0][1] = DegreeSin(degrees)); ConsiderContext(obj, M); return(Xform(obj, M)); } #endif /* :h3.PseudoSpace() - Build a Coordinate Space from a Matrix Since we have built all this optimized code that, given an (x,y) and a coordinate space, yield transformed (x,y), it seems a shame not to use the same logic when we need to multiply an (x,y) by an arbitrary matrix that is not (initially) part of a coordinate space. This subroutine takes the arbitrary matrix and builds a coordinate space, with all its nifty function pointers. */ void PseudoSpace(struct XYspace *S, /* coordinate space structure to fill out */ double M[2][2]) /* matrix that will become 'tofract.normal' */ { S->type = SPACETYPE; S->flag = ISPERMANENT(ON) + ISIMMORTAL(ON); S->references = 2; /* 3-26-91 added PNM */ S->tofract.normal[0][0] = M[0][0]; S->tofract.normal[1][0] = M[1][0]; S->tofract.normal[0][1] = M[0][1]; S->tofract.normal[1][1] = M[1][1]; FillOutFcns(S); } /* :h2 id=matrixa.Matrix Arithmetic Following the convention in Newman and Sproull, :hp1/Interactive Computer Graphics/, matrices are organized: :xmp. | cxx cyx | | cxy cyy | :exmp. A point is horizontal, for example: :xmp. [ x y ] :exmp. This means that: :formula/x prime = cxx times x + cxy times y/ :formula/y prime = cyx times x + cyy times y/ I've seen the other convention, where transform matrices are transposed, equally often in the literature. */ /* :h3.MatrixMultiply() - Implements Multiplication of Two Matrices Implements matrix multiplication, A * B = C. To remind myself, matrix multiplication goes rows of A times columns of B. The output matrix may be the same as one of the input matrices. */ void MatrixMultiply(double A[2][2], double B[2][2], /* input matrices */ double C[2][2]) /* output matrix */ { register double txx,txy,tyx,tyy; txx = A[0][0] * B[0][0] + A[0][1] * B[1][0]; txy = A[1][0] * B[0][0] + A[1][1] * B[1][0]; tyx = A[0][0] * B[0][1] + A[0][1] * B[1][1]; tyy = A[1][0] * B[0][1] + A[1][1] * B[1][1]; C[0][0] = txx; C[1][0] = txy; C[0][1] = tyx; C[1][1] = tyy; } /* :h3.MatrixInvert() - Invert a Matrix My reference for matrix inversion was :hp1/Elementary Linear Algebra/ by Paul C. Shields, Worth Publishers, Inc., 1968. */ void MatrixInvert(double M[2][2], /* input matrix */ double Mprime[2][2]) /* output inverted matrix */ { register double D; /* determinant of matrix M */ register double txx,txy,tyx,tyy; txx = M[0][0]; txy = M[1][0]; tyx = M[0][1]; tyy = M[1][1]; D = M[1][1] * M[0][0] - M[1][0] * M[0][1]; if (D == 0.0) Abort("MatrixInvert: can't"); Mprime[0][0] = tyy / D; Mprime[1][0] = -txy / D; Mprime[0][1] = -tyx / D; Mprime[1][1] = txx / D; } /* :h2.Initialization, Queries, and Debug */ /* :h3.InitSpaces() - Initialize Constant Spaces For compatibility, we initialize a coordinate space called USER which maps 72nds of an inch to pels on the default device. */ struct XYspace *USER = &identity; void InitSpaces(void) { IDENTITY->type = SPACETYPE; FillOutFcns(IDENTITY); contexts[NULLCONTEXT].normal[1][0] = contexts[NULLCONTEXT].normal[0][1] = contexts[NULLCONTEXT].inverse[1][0] = contexts[NULLCONTEXT].inverse[0][1] = 0.0; contexts[NULLCONTEXT].normal[0][0] = contexts[NULLCONTEXT].normal[1][1] = contexts[NULLCONTEXT].inverse[0][0] = contexts[NULLCONTEXT].inverse[1][1] = 1.0; USER->flag |= ISIMMORTAL(ON); CoerceInverse(USER); } /* :h3.QuerySpace() - Returns the Transformation Matrix of a Space Since the tofract matrix of an XYspace includes the scale factor necessary to produce fractpel results (i.e., FRACTFLOAT), this must be taken out before we return the matrix to the user. Fortunately, this is simple: just multiply by the inverse of IDENTITY! */ void QuerySpace(struct XYspace *S, /* space asked about */ double *cxxP, double *cyxP, /* where to put answer */ double *cxyP, double *cyyP) { double M[2][2]; /* temp matrix to build user's answer */ if (S->type != SPACETYPE) { ArgErr("QuerySpace: not a space", S, NULL); return; } MatrixMultiply(S->tofract.normal, IDENTITY->tofract.inverse, M); *cxxP = M[0][0]; *cxyP = M[1][0]; *cyxP = M[0][1]; *cyyP = M[1][1]; } /* :h3.FormatFP() - Format a Fixed Point Pel We format the pel as "dddd.XXXX", where XX's are hexidecimal digits, and the dd's are decimal digits. This might be a little confusing mixing hexidecimal and decimal like that, but it is convenient to use for debug. We make sure we have N (FRACTBITS/4) digits past the decimal point. */ #define FRACTMASK ((1<<FRACTBITS)-1) /* mask for fractional part */ void FormatFP(char *string, /* output string */ fractpel fpel) /* fractional pel input */ { char temp[8]; register char *s; register char *sign; if (fpel < 0) { sign = "-"; fpel = -fpel; } else sign = ""; sprintf(temp, "000%lx", fpel & FRACTMASK); s = temp + strlen(temp) - (FRACTBITS/4); sprintf(string, "%s%d.%sx", sign, (int)(fpel >> FRACTBITS), s); } /* :h3.DumpSpace() - Display a Coordinate Space */ /*ARGSUSED*/ void DumpSpace(struct XYspace *S) { }