From f4092abdf94af6a99aff944d6264bc1284e8bdd4 Mon Sep 17 00:00:00 2001 From: Reinhard Tartler Date: Mon, 10 Oct 2011 17:43:39 +0200 Subject: Imported nx-X11-3.1.0-1.tar.gz Summary: Imported nx-X11-3.1.0-1.tar.gz Keywords: Imported nx-X11-3.1.0-1.tar.gz into Git repository --- nx-X11/lib/font/Type1/spaces.c | 998 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 998 insertions(+) create mode 100644 nx-X11/lib/font/Type1/spaces.c (limited to 'nx-X11/lib/font/Type1/spaces.c') diff --git a/nx-X11/lib/font/Type1/spaces.c b/nx-X11/lib/font/Type1/spaces.c new file mode 100644 index 000000000..55cc96f67 --- /dev/null +++ b/nx-X11/lib/font/Type1/spaces.c @@ -0,0 +1,998 @@ +/* $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 3.10tsi 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 HAVE_CONFIG_H +#include +#endif +#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 +#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<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), s); +} + +/* +:h3.DumpSpace() - Display a Coordinate Space +*/ +/*ARGSUSED*/ +void +DumpSpace(struct XYspace *S) +{ +} -- cgit v1.2.3