tktrig.c

linux系统下的音频通信

 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

void
TkBezierPoints(control, numSteps, coordPtr)
    double control[];			/* Array of coordinates for four
					 * control points:  x0, y0, x1, y1,
					 * ... x3 y3. */
    int numSteps;			/* Number of curve points to
					 * generate.  */
    register double *coordPtr;		/* Where to put new points. */
{
    int i;
    double u, u2, u3, t, t2, t3;

    for (i = 1; i <= numSteps; i++, coordPtr += 2) {
	t = ((double) i)/((double) numSteps);
	t2 = t*t;
	t3 = t2*t;
	u = 1.0 - t;
	u2 = u*u;
	u3 = u2*u;
	coordPtr[0] = control[0]*u3
		+ 3.0 * (control[2]*t*u2 + control[4]*t2*u) + control[6]*t3;
	coordPtr[1] = control[1]*u3
		+ 3.0 * (control[3]*t*u2 + control[5]*t2*u) + control[7]*t3;
    }
}

/*
 *--------------------------------------------------------------
 *
 * TkMakeBezierCurve --
 *
 *	Given a set of points, create a new set of points that fit
 *	parabolic splines to the line segments connecting the original
 *	points.  Produces output points in either of two forms.
 *
 *	Note: in spite of this procedure's name, it does *not* generate
 *	Bezier curves.  Since only three control points are used for
 *	each curve segment, not four, the curves are actually just
 *	parabolic.
 *
 * Results:
 *	Either or both of the xPoints or dblPoints arrays are filled
 *	in.  The return value is the number of points placed in the
 *	arrays.  Note:  if the first and last points are the same, then
 *	a closed curve is generated.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

int
TkMakeBezierCurve(canvas, pointPtr, numPoints, numSteps, xPoints, dblPoints)
    Tk_Canvas canvas;			/* Canvas in which curve is to be
					 * drawn. */
    double *pointPtr;			/* Array of input coordinates:  x0,
					 * y0, x1, y1, etc.. */
    int numPoints;			/* Number of points at pointPtr. */
    int numSteps;			/* Number of steps to use for each
					 * spline segments (determines
					 * smoothness of curve). */
    XPoint xPoints[];			/* Array of XPoints to fill in (e.g.
					 * for display.  NULL means don't
					 * fill in any XPoints. */
    double dblPoints[];			/* Array of points to fill in as
					 * doubles, in the form x0, y0,
					 * x1, y1, ....  NULL means don't
					 * fill in anything in this form. 
					 * Caller must make sure that this
					 * array has enough space. */
{
    int closed, outputPoints, i;
    int numCoords = numPoints*2;
    double control[8];

    /*
     * If the curve is a closed one then generate a special spline
     * that spans the last points and the first ones.  Otherwise
     * just put the first point into the output.
     */

    outputPoints = 0;
    if ((pointPtr[0] == pointPtr[numCoords-2])
	    && (pointPtr[1] == pointPtr[numCoords-1])) {
	closed = 1;
	control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0];
	control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1];
	control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0];
	control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1];
	control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2];
	control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3];
	control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
	control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
	if (xPoints != NULL) {
	    Tk_CanvasDrawableCoords(canvas, control[0], control[1],
		    &xPoints->x, &xPoints->y);
	    TkBezierScreenPoints(canvas, control, numSteps, xPoints+1);
	    xPoints += numSteps+1;
	}
	if (dblPoints != NULL) {
	    dblPoints[0] = control[0];
	    dblPoints[1] = control[1];
	    TkBezierPoints(control, numSteps, dblPoints+2);
	    dblPoints += 2*(numSteps+1);
	}
	outputPoints += numSteps+1;
    } else {
	closed = 0;
	if (xPoints != NULL) {
	    Tk_CanvasDrawableCoords(canvas, pointPtr[0], pointPtr[1],
		    &xPoints->x, &xPoints->y);
	    xPoints += 1;
	}
	if (dblPoints != NULL) {
	    dblPoints[0] = pointPtr[0];
	    dblPoints[1] = pointPtr[1];
	    dblPoints += 2;
	}
	outputPoints += 1;
    }

    for (i = 2; i < numPoints; i++, pointPtr += 2) {
	/*
	 * Set up the first two control points.  This is done
	 * differently for the first spline of an open curve
	 * than for other cases.
	 */

	if ((i == 2) && !closed) {
	    control[0] = pointPtr[0];
	    control[1] = pointPtr[1];
	    control[2] = 0.333*pointPtr[0] + 0.667*pointPtr[2];
	    control[3] = 0.333*pointPtr[1] + 0.667*pointPtr[3];
	} else {
	    control[0] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
	    control[1] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
	    control[2] = 0.167*pointPtr[0] + 0.833*pointPtr[2];
	    control[3] = 0.167*pointPtr[1] + 0.833*pointPtr[3];
	}

	/*
	 * Set up the last two control points.  This is done
	 * differently for the last spline of an open curve
	 * than for other cases.
	 */

	if ((i == (numPoints-1)) && !closed) {
	    control[4] = .667*pointPtr[2] + .333*pointPtr[4];
	    control[5] = .667*pointPtr[3] + .333*pointPtr[5];
	    control[6] = pointPtr[4];
	    control[7] = pointPtr[5];
	} else {
	    control[4] = .833*pointPtr[2] + .167*pointPtr[4];
	    control[5] = .833*pointPtr[3] + .167*pointPtr[5];
	    control[6] = 0.5*pointPtr[2] + 0.5*pointPtr[4];
	    control[7] = 0.5*pointPtr[3] + 0.5*pointPtr[5];
	}

	/*
	 * If the first two points coincide, or if the last
	 * two points coincide, then generate a single
	 * straight-line segment by outputting the last control
	 * point.
	 */

	if (((pointPtr[0] == pointPtr[2]) && (pointPtr[1] == pointPtr[3]))
		|| ((pointPtr[2] == pointPtr[4])
		&& (pointPtr[3] == pointPtr[5]))) {
	    if (xPoints != NULL) {
		Tk_CanvasDrawableCoords(canvas, control[6], control[7],
			&xPoints[0].x, &xPoints[0].y);
		xPoints++;
	    }
	    if (dblPoints != NULL) {
		dblPoints[0] = control[6];
		dblPoints[1] = control[7];
		dblPoints += 2;
	    }
	    outputPoints += 1;
	    continue;
	}

	/*
	 * Generate a Bezier spline using the control points.
	 */


	if (xPoints != NULL) {
	    TkBezierScreenPoints(canvas, control, numSteps, xPoints);
	    xPoints += numSteps;
	}
	if (dblPoints != NULL) {
	    TkBezierPoints(control, numSteps, dblPoints);
	    dblPoints += 2*numSteps;
	}
	outputPoints += numSteps;
    }
    return outputPoints;
}

/*
 *--------------------------------------------------------------
 *
 * TkMakeBezierPostscript --
 *
 *	This procedure generates Postscript commands that create
 *	a path corresponding to a given Bezier curve.
 *
 * Results:
 *	None.  Postscript commands to generate the path are appended
 *	to interp->result.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

void
TkMakeBezierPostscript(interp, canvas, pointPtr, numPoints)
    Tcl_Interp *interp;			/* Interpreter in whose result the
					 * Postscript is to be stored. */
    Tk_Canvas canvas;			/* Canvas widget for which the
					 * Postscript is being generated. */
    double *pointPtr;			/* Array of input coordinates:  x0,
					 * y0, x1, y1, etc.. */
    int numPoints;			/* Number of points at pointPtr. */
{
    int closed, i;
    int numCoords = numPoints*2;
    double control[8];
    char buffer[200];

    /*
     * If the curve is a closed one then generate a special spline
     * that spans the last points and the first ones.  Otherwise
     * just put the first point into the path.
     */

    if ((pointPtr[0] == pointPtr[numCoords-2])
	    && (pointPtr[1] == pointPtr[numCoords-1])) {
	closed = 1;
	control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0];
	control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1];
	control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0];
	control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1];
	control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2];
	control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3];
	control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
	control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
	sprintf(buffer, "%.15g %.15g moveto\n%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
		control[0], Tk_CanvasPsY(canvas, control[1]),
		control[2], Tk_CanvasPsY(canvas, control[3]),
		control[4], Tk_CanvasPsY(canvas, control[5]),
		control[6], Tk_CanvasPsY(canvas, control[7]));
    } else {
	closed = 0;
	control[6] = pointPtr[0];
	control[7] = pointPtr[1];
	sprintf(buffer, "%.15g %.15g moveto\n",
		control[6], Tk_CanvasPsY(canvas, control[7]));
    }
    Tcl_AppendResult(interp, buffer, (char *) NULL);

    /*
     * Cycle through all the remaining points in the curve, generating
     * a curve section for each vertex in the linear path.
     */

    for (i = numPoints-2, pointPtr += 2; i > 0; i--, pointPtr += 2) {
	control[2] = 0.333*control[6] + 0.667*pointPtr[0];
	control[3] = 0.333*control[7] + 0.667*pointPtr[1];

	/*
	 * Set up the last two control points.  This is done
	 * differently for the last spline of an open curve
	 * than for other cases.
	 */

	if ((i == 1) && !closed) {
	    control[6] = pointPtr[2];
	    control[7] = pointPtr[3];
	} else {
	    control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2];
	    control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3];
	}
	control[4] = 0.333*control[6] + 0.667*pointPtr[0];
	control[5] = 0.333*control[7] + 0.667*pointPtr[1];

	sprintf(buffer, "%.15g %.15g %.15g %.15g %.15g %.15g curveto\n",
		control[2], Tk_CanvasPsY(canvas, control[3]),
		control[4], Tk_CanvasPsY(canvas, control[5]),
		control[6], Tk_CanvasPsY(canvas, control[7]));
	Tcl_AppendResult(interp, buffer, (char *) NULL);
    }
}

/*
 *--------------------------------------------------------------
 *
 * TkGetMiterPoints --
 *
 *	Given three points forming an angle, compute the
 *	coordinates of the inside and outside points of
 *	the mitered corner formed by a line of a given
 *	width at that angle.
 *
 * Results:
 *	If the angle formed by the three points is less than
 *	11 degrees then 0 is returned and m1 and m2 aren't
 *	modified.  Otherwise 1 is returned and the points at
 *	m1 and m2 are filled in with the positions of the points
 *	of the mitered corner.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

int
TkGetMiterPoints(p1, p2, p3, width, m1, m2)
    double p1[];		/* Points to x- and y-coordinates of point
				 * before vertex. */
    double p2[];		/* Points to x- and y-coordinates of vertex
				 * for mitered joint. */
    double p3[];		/* Points to x- and y-coordinates of point
				 * after vertex. */
    double width;		/* Width of line.  */
    double m1[];		/* Points to place to put "left" vertex
				 * point (see as you face from p1 to p2). */
    double m2[];		/* Points to place to put "right" vertex
				 * point. */
{
    double theta1;		/* Angle of segment p2-p1. */
    double theta2;		/* Angle of segment p2-p3. */
    double theta;		/* Angle between line segments (angle
				 * of joint). */
    double theta3;		/* Angle that bisects theta1 and
				 * theta2 and points to m1. */
    double dist;		/* Distance of miter points from p2. */
    double deltaX, deltaY;	/* X and y offsets cooresponding to
				 * dist (fudge factors for bounding
				 * box). */
    double p1x, p1y, p2x, p2y, p3x, p3y;
    static double elevenDegrees = (11.0*2.0*PI)/360.0;

    /*
     * Round the coordinates to integers to mimic what happens when the
     * line segments are displayed; without this code, the bounding box
     * of a mitered line can be miscomputed greatly.
     */

    p1x = floor(p1[0]+0.5);
    p1y = floor(p1[1]+0.5);
    p2x = floor(p2[0]+0.5);
    p2y = floor(p2[1]+0.5);
    p3x = floor(p3[0]+0.5);
    p3y = floor(p3[1]+0.5);

    if (p2y == p1y) {
	theta1 = (p2x < p1x) ? 0 : PI;
    } else if (p2x == p1x) {
	theta1 = (p2y < p1y) ? PI/2.0 : -PI/2.0;
    } else {
	theta1 = atan2(p1y - p2y, p1x - p2x);
    }
    if (p3y == p2y) {
	theta2 = (p3x > p2x) ? 0 : PI;
    } else if (p3x == p2x) {
	theta2 = (p3y > p2y) ? PI/2.0 : -PI/2.0;
    } else {
	theta2 = atan2(p3y - p2y, p3x - p2x);
    }
    theta = theta1 - theta2;
    if (theta > PI) {
	theta -= 2*PI;
    } else if (theta < -PI) {
	theta += 2*PI;
    }
    if ((theta < elevenDegrees) && (theta > -elevenDegrees)) {
	return 0;
    }
    dist = 0.5*width/sin(0.5*theta);
    if (dist < 0.0) {
	dist = -dist;
    }

    /*
     * Compute theta3 (make sure that it points to the left when
     * looking from p1 to p2).
     */

    theta3 = (theta1 + theta2)/2.0;
    if (sin(theta3 - (theta1 + PI)) < 0.0) {
	theta3 += PI;
    }
    deltaX = dist*cos(theta3);
    m1[0] = p2x + deltaX;
    m2[0] = p2x - deltaX;
    deltaY = dist*sin(theta3);
    m1[1] = p2y + deltaY;
    m2[1] = p2y - deltaY;
    return 1;
}

/*
 *--------------------------------------------------------------
 *
 * TkGetButtPoints --
 *
 *	Given two points forming a line segment, compute the
 *	coordinates of two endpoints of a rectangle formed by
 *	bloating the line segment until it is width units wide.
 *
 * Results:
 *	There is no return value.  M1 and m2 are filled in to
 *	correspond to m1 and m2 in the diagram below:
 *
 *		   ----------------* m1
 *				   |
 *		p1 *---------------* p2
 *				   |
 *		   ----------------* m2
 *
 *	M1 and m2 will be W units apart, with p2 centered between
 *	them and m1-m2 perpendicular to p1-p2.  However, if
 *	"project" is true then m1 and m2 will be as follows:
 *
 *		   -------------------* m1
 *				  p2  |
 *		p1 *---------------*  |
 *				      |
 *		   -------------------* m2
 *
 *	In this case p2 will be width/2 units from the segment m1-m2.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

void
TkGetButtPoints(p1, p2, width, project, m1, m2)
    double p1[];		/* Points to x- and y-coordinates of point
				 * before vertex. */
    double p2[];		/* Points to x- and y-coordinates of vertex
				 * for mitered joint. */
    double width;		/* Width of line.  */
    int project;		/* Non-zero means project p2 by an additional
				 * width/2 before computing m1 and m2. */
    double m1[];		/* Points to place to put "left" result
				 * point, as you face from p1 to p2. */
    double m2[];		/* Points to place to put "right" result
				 * point. */
{
    double length;		/* Length of p1-p2 segment. */
    double deltaX, deltaY;	/* Increments in coords. */

    width *= 0.5;
    length = hypot(p2[0] - p1[0], p2[1] - p1[1]);
    if (length == 0.0) {
	m1[0] = m2[0] = p2[0];
	m1[1] = m2[1] = p2[1];
    } else {
	deltaX = -width * (p2[1] - p1[1]) / length;
	deltaY = width * (p2[0] - p1[0]) / length;
	m1[0] = p2[0] + deltaX;
	m2[0] = p2[0] - deltaX;
	m1[1] = p2[1] + deltaY;
	m2[1] = p2[1] - deltaY;
	if (project) {
	    m1[0] += deltaY;
	    m2[0] += deltaY;
	    m1[1] -= deltaX;
	    m2[1] -= deltaX;
	}
    }
}