# Note:
#    The list xyvalues must be sorted w.r.t. the x-value
#
proc ::math::interpolate::interp-linear { xyvalues xval } {
   #
   # Border cases first
   #
   if { [lindex $xyvalues 0]+0.0 > $xval } {
      return [lindex $xyvalues 1]
   }
   if { [lindex $xyvalues end-1]+0.0 < $xval } {
      return [lindex $xyvalues end]
   }

   #
   # The ordinary case
   #
   set idxx -2
   set idxy -1
   foreach { x y } $xyvalues {
      if { $xval < $x } {
         break
      }
      incr idxx 2
      incr idxy 2
   }

   set x2 [lindex $xyvalues $idxx]
   set y2 [lindex $xyvalues $idxy]

   if { $x2 != $x } {
      set yval [expr {$y+($y2-$y)*($xval-$x)/double($x2-$x)}]
   } else {
      set yval [expr {double($y)}]
   }
   return $yval
}

# interp-lagrange --
#    Use the Lagrange interpolation method
#

}



#
# Announce our presence
#
package provide math::interpolate 1.1.2

package ifneeded math::fourier           1.0.2 [list source [file join $dir fourier.tcl]]

if {![package vsatisfies [package provide Tcl] 8.3]} {return}
package ifneeded math::roman             1.0   [list source [file join $dir romannumerals.tcl]]

if {![package vsatisfies [package provide Tcl] 8.4]} {return}
package ifneeded math::optimize          1.0.1 [list source [file join $dir optimize.tcl]]
package ifneeded math::interpolate       1.1.2 [list source [file join $dir interpolate.tcl]]
package ifneeded math::bignum            3.1.1 [list source [file join $dir bignum.tcl]]
package ifneeded math::bigfloat          1.2.2 [list source [file join $dir bigfloat.tcl]]
package ifneeded math::machineparameters 0.1   [list source [file join $dir machineparameters.tcl]]

if {![package vsatisfies [package provide Tcl] 8.5]} {return}
package ifneeded math::calculus          0.8.1 [list source [file join $dir calculus.tcl]]
# statistics depends on linearalgebra (for multi-variate linear regression).

	bind $canvas <Double-ButtonRelease-1> \
	    [namespace code {my Double1 %x %y}]

	bind $canvas <Control-B1-Motion> {;}
	bind $canvas <Shift-B1-Motion>	[namespace code {my ShiftMotion1 %x %y}]

	if {[tk windowingsystem] eq "aqua"} {
	    bind $canvas <Shift-MouseWheel>	[namespace code {my MouseWheel [expr {40 * (%D)}]}]
	    bind $canvas <Option-Shift-MouseWheel>	[namespace code {my MouseWheel [expr {400 * (%D)}]}]
	} else {
	    bind $canvas <Shift-MouseWheel>	[namespace code {my MouseWheel %D}]
	}
	if {[tk windowingsystem] eq "x11"} {
	    bind $canvas <Shift-4>	[namespace code {my MouseWheel 120}]
	    bind $canvas <Shift-5>	[namespace code {my MouseWheel -120}]
	}

	bind $canvas <<PrevLine>>	[namespace code {my UpDown -1}]

        %W xview scroll [expr {-(%D)}] units
    }
    bind Listbox <Shift-Option-MouseWheel> {
        %W xview scroll [expr {-10 * (%D)}] units
    }
} else {
    bind Listbox <MouseWheel> {
	if {%D >= 0} {
	    %W yview scroll [expr {-%D/30}] units
	} else {
	    %W yview scroll [expr {(29-%D)/30}] units
	}
    }
    bind Listbox <Shift-MouseWheel> {
	if {%D >= 0} {
	    %W xview scroll [expr {-%D/30}] units
	} else {
	    %W xview scroll [expr {(29-%D)/30}] units
	}
    }
}

if {[tk windowingsystem] eq "x11"} {
    # Support for mousewheels on Linux/Unix commonly comes through mapping
    # the wheel to the extended buttons.  If you have a mousewheel, find
    # Linux configuration info at:

bind Scrollbar <<LineStart>> {
    tk::ScrollToPos %W 0
}
bind Scrollbar <<LineEnd>> {
    tk::ScrollToPos %W 1
}
}

if {[tk windowingsystem] eq "aqua"} {

    bind Scrollbar <MouseWheel> {
	tk::ScrollByUnits %W v [expr {-(%D)}]
    }
    bind Scrollbar <Option-MouseWheel> {
	tk::ScrollByUnits %W v [expr {-10 * (%D)}]
    }
    bind Scrollbar <Shift-MouseWheel> {
	tk::ScrollByUnits %W h [expr {-(%D)}]
    }
    bind Scrollbar <Shift-Option-MouseWheel> {
	tk::ScrollByUnits %W h [expr {-10 * (%D)}]
    }
} else {

    bind Scrollbar <MouseWheel> {
	if {%D >= 0} {
	    tk::ScrollByUnits %W v [expr {-%D/30}]
	} else {
	    tk::ScrollByUnits %W v [expr {(29-%D)/30}]
	}
    }
    bind Scrollbar <Shift-MouseWheel> {
	if {%D >= 0} {
	    tk::ScrollByUnits %W h [expr {-%D/30}]
	} else {
	    tk::ScrollByUnits %W h [expr {(29-%D)/30}]
	}
    }



}



if {[tk windowingsystem] eq "x11"} {
    bind Scrollbar <4> {tk::ScrollByUnits %W v -5}
    bind Scrollbar <5> {tk::ScrollByUnits %W v 5}
    bind Scrollbar <Shift-4> {tk::ScrollByUnits %W h -5}
    bind Scrollbar <Shift-5> {tk::ScrollByUnits %W h 5}
}

# tk::ScrollButtonDown --
# This procedure is invoked when a button is pressed in a scrollbar.
# It changes the way the scrollbar is displayed and takes actions
# depending on where the mouse is.
#
# Arguments:
# w -		The scrollbar widget.

	/*
	 * We can only draw into the view when the current CGContext is valid
	 * and belongs to the view.  Validity can only be guaranteed inside of
	 * a view's drawRect or setFrame methods.  The isDrawing attribute
	 * tells us whether we are being called from one of those methods.
	 *
	 * If the CGContext is not valid then we mark our view as needing
	 * display in the bounding rectangle of the clipping region and
	 * return failure.  That rectangle should get drawn in a later call
	 * to drawRect.
	 */
 
	if (![NSApp isDrawing] || view != [NSView focusView]) {
	    NSRect bounds = [view bounds];
	    NSRect dirtyNS = bounds;
	    CGAffineTransform t = { .a = 1, .b = 0, .c = 0, .d = -1, .tx = 0,
				    .ty = dirtyNS.size.height};
	    if (dc.clipRgn) {
		CGRect dirtyCG = NSRectToCGRect(dirtyNS);
		HIShapeGetBounds(dc.clipRgn, &dirtyCG);
		dirtyNS = NSRectToCGRect(CGRectApplyAffineTransform(dirtyCG, t));
	    }
	    [view setNeedsDisplayInRect:dirtyNS];
	    canDraw = false;
	    goto end;
	}
 
	dc.view = view;
	dc.context = GET_CGCONTEXT;
	dc.portBounds = NSRectToCGRect([view bounds]);
	if (dc.clipRgn) {
	    clipBounds = CGContextGetClipBoundingBox(dc.context);
	}
    } else {

		CreateNamedSystemFont(interp, tkwin, systemFont->tkName1, &fa);
	    }
	    CFRelease(nsFont);
	}
	systemFont++;
    }
    TkInitFontAttributes(&fa);
#if 0
    /*
     * In macOS 10.15.1 Apple introduced a bug which caused the call below to
     * return a font with the invalid familyName ".SF NSMono" instead of the
     * valid familyName "NSMono". Calling [NSFont userFixedPitchFontOfSize:11]
     * returns a font in the "Menlo" family which has a valid familyName.
     */  
    nsFont = (NSFont*) CTFontCreateUIFontForLanguage(fixedPitch, 11, NULL);
#else
    nsFont = [NSFont userFixedPitchFontOfSize:11];
#endif
    if (nsFont) {
	GetTkFontAttributesForNSFont(nsFont, &fa);
#if 0
	CFRelease(nsFont);
#endif
    } else {
	fa.family = Tk_GetUid("Monaco");
	fa.size = 11;
	fa.weight = TK_FW_NORMAL;
	fa.slant = TK_FS_ROMAN;
    }
    CreateNamedSystemFont(interp, tkwin, "TkFixedFont", &fa);