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#X text 143 577 2) float;
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#X text 143 560 1) symbol;
#X text 125 502 float/signal;
#X text 125 482 float/signal;
#X text 213 502 - set endpoint (in ms), f 54;
#X text 213 482 - set startpoint (in ms), f 54;
#X text 213 577 - startpoint in ms (default 0), f 54;
#X text 125 412 set <symbol>;
#X text 213 412 - sets array name, f 54;
#X text 113 428 interp <float>;
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#X text 51 312 The cosine interpolator maps a cosine curve (from phase 0 to phase pi) to the values it is interpolating between. It is of limited use., f 76;
#X text 45 150 As indices in an array increase \, there is less and less index resolution between integer index values. The low-quality linear interpolation maps the 0.0-1.0 phase range to the array range in single precision \, which means that low index resolution later in the table can result in lower quality audio. The high-quality linear interpolation handles all index values as well as values read from the table in double precision \, so that the 24-bit resolution between 0 and 1 is preserved no matter where in the table it reads from., f 76;
#X text 49 122 Modes 1 & 2 (High & Low Quality Linear Interpolation \, respectively):, f 69;
#X text 49 63 mode 0 (no interpolation):, f 76;
#X text 51 88 there is no interpolation \, this means that indexes are truncated to the sample point., f 73;
#X text 41 282 Mode 3 Cosine Interpolation):;
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#X text 24 283 The advantage of Lagrange interpolation is that the curve drawn has low RMS error with respect to that of an ideal (sinc) interpolator. A disadvantage is that the first derivative (the isntantaneous slope of the curve) is not usually continuous at breakpoints \, which can cause sharp corners in the curve (see examples in the parent patch)., f 75;
#X text 24 396 An Hermite interpolator addresses the first derivative problem with the Lagrange by deliberately making the first derivative continuous at breakpoints. It interpolates between b and c by finding a cubic polynomial curve that passes through b and c. The curve does not usually pass through a and d. Instead \, the interpolator uses the pairs (a \, c) and (b \, d) to set the curve slope at points b and c \, respectively., f 75;
#X text 25 187 To interpolate between points b and c \, a Lagrange interpolator finds a cubic polynomial curve f(x) that passes through all four points a \, b \, c \, and d \, imagining a = f(-1) \, b = f(0) \, c = f(1) \, and d = f(2)., f 75;
#X text 24 235 This is the the kind of interpolation used in Pd's [tabread4~] \, as well as the cubic interpolating functions in csound. The output is f(m) (where m is the fractional index between 0 and 1)., f 75;
#X text 514 37 The most basic form of Hermite interpolator sets the curve slope at point b as the slope of the line passing through a and c \, which is defined (c - a)/2. The curve slope at point c is set to (d - b)/2. In the examples \, it is easy to see that there are no sharp corners. However \, the second derivative is discontinuous \, so there are occasional abrupt changes in concavity \, e.g. at zero-crossings in the 4-period cosine example. There are no such abrupt changes in concavity with Lagrange interpolation. This type of interpolation is used in SuperCollider's interpolating functions., f 75;
#X text 514 459 The normal range for both tension and bias values is -1 to +1. Outside of that range the curves can be unpredictable., f 75;
#X text 21 86 The four cubic interpolators work differently from one another. They are discussed out of order here for the sake of clarity. For all examples \, let us label the four points as: a \, b \, c \, and d \, with interpolation between points b and c., f 76;
#X text 21 38 Cubic interpolation draws a cubic polynomial curve between the two points it is interpolating between \, and uses the points to the left and right of these two as extra information to draw these curves., f 76;
#X text 514 220 Other slope values can be used to accentuate or attenuate the shape of the curve. The "tension" setting in mode 6 adjusts the curve slope at breakpoints. At point b \, the slope is (1 - tension)*((c - a)/2). A tension value of 0 is identical to the Catmull-Rom spline (Mode 5). When tension is +1 \, the slope is 0 (horizontal) at all breakpoints. Between 0 and 1 \, the slope at breakpoints is less than that for the Catmull-Rom spline \, and the maxima and curve is shallower., f 75;
#X text 514 317 Tension values between 0 and -1 increase the slope at breakpoints and make the curve deeper. At tension = -1 \, the slope at breakpoints is double that of the Catmull-Rom spline \, and the curve is identical to the "Cubic" interpolation (Mode 4). The period-8 cosine example in the [pd examples] subpatch is a good illustration of tension., f 75;
#X text 514 389 Bias is related to tension in that it changes slope at breakpoints and depth of curve \, but it does so by giving one of the two points surrounding the breakpoint more control over the slope at that breakpoint than the other. Bias values between 0 and 1 give the left point more influence than the right \, bias values between 0 and -1 do the opposite., f 75;
#X text 22 18 Overview:;
#X text 24 157 Mode 7: Pd's Cubic Interpolator (Lagrange):;
#X text 26 372 Modes 4 \, 5 & 6: Hermite Interpolators;
#X text 516 19 Catmull-Rom Spline (mode 5);
#X text 518 146 (modes 4 and 6):;
#X text 525 166 Mode 6: With settable Tension and Bias;
#X text 528 187 Mode 4: "Cubic" \, with tension of -1;
#X restore 319 320 pd cubic (modes 4 to 7);
#X text 19 17 Though not referred in Max's documentation \, the interpolation formulas for [wave~] almost certainly can found in <http://paulbourke.net/miscellaneous/interpolation>., f 82;
#X text 19 50 [wave~]'s input phase varies between 0 and 1 \, which in 32-bit floating point arithmetic has 24 bits of index resolution. All interpolators (except mode 2: low quality linear) use double-precision index mapping \, so behavior should be the same in all parts of a table., f 82;
#X text 19 185 Backwards compatibility:, f 82;
#X text 19 209 At the time of Max 4 \, [wave~] only had one cheaop linear interpolator. Earlier versions of cyclone included Pd's interpolator isntead. This is mode is now added as an extra mode 7 (and is also used in [tabread4~] \, [tabosc4~] \, and [vd~] or [delread4~])., f 82;
#X text 20 280 Please find more theoretical details for each mode in the subpatches below:, f 82;
#X text 19 108 Unlike [tabread4~] \, [wave~] does not use guard points for interpolating between the end and the beginning of the array \, but isntead treats the range as a circular buffer \, where phases 0 and 1 point to the first element of the table. Input phase is clipped to the 0-1 range. A bug from Max was fixed \, where the 4-point interpolation modes did not wrap correctly., f 82;
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#X restore 259 334 pd examples;
#X text 77 85 0 - No interpolation, f 47;
#X text 77 101 1 - High-quality linear interpolation (default);
#X text 77 119 2 -;
#X text 101 118 Low-quality linear interpolation (found in MSP 1.x versions of [wave~], f 43;
#X text 77 147 3 - Cosine interpolation, f 47;
#X text 77 164 4 - Cubic interpolation, f 47;
#X text 77 180 5 - Spline interpolation, f 47;
#X text 77 196 6 - Hermite interpolation, f 47;
#X text 77 212 7 - Extra: Pd's interpolator (Lagrange), f 47;
#X text 40 29 The [wave~] object in cyclone offers 7 modes of interpolation \, which can be set with the "interp" message/attribute., f 62;
#X text 41 60 The modes are:;
#X text 41 241 The Hermite interpolation has extra parameters: 'bias' and 'tension' \, respectively set with the 'interp_bias' and 'interp_tension' messages/attributes.;
#X text 41 290 For more details in the theory of interpolation and some examples \, please check the subopatches below:, f 58;
#X text 101 366 Information and examples provided by Matt Barber;
#X restore 406 235 pd interpolation_modes;
#X text 89 460 interp_tension <f>;
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#X text 107 444 interp_bias <f>;
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#X text 213 594 - endpoint in ms (default is length of array in ms), f 54;
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#X text 170 330 keeps start slider before end slider;
#X obj 46 337 moses;
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#X text 97 90 max array index;
#X text 36 141 array length in ms;
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#X msg 164 201 set \$1;
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#X text 317 228 <= set sliders;
#X text 170 345 and keeps end slider after start slider;
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#X text 89 53 Using [wave~] to read a sample file;
#X obj 75 261 output~;
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#X text 38 80 If more than one channel is set \, the name convention for multi channel arrays is the table name preceded by the channel number (starting from zero) and "-" \, such as: "0-" \, "1-" \, "2-" \, "3-" \, and so on...;
#X text 41 151 You can manually set multi channel arrays in Pd like that or use the [buffer~] object \, which does this internally.;
#X msg 457 152 open;
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#X text 38 28 Multi channel playback is possible (up to 64 channels) when you specify it with a 4th argument. The number of channels defines the number 'n' of outlets.;
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#X text 78 83 With a phase signal input (from 0 and 1) \, [wave~] reads a given table. It has many interpolation options and can set a start and end point in the array.;
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#X text 35 19 [wave~] as a table reader;
#X text 112 66 <= index;
#X text 52 196 table value;
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#X restore 431 162 pd tabread_example;
#X text 64 179 as a wavetable oscillator ====>, f 17;
#X text 213 533 - the specified portion of the given wavetable channel;
#X text 213 428 - set inpterpolation modes <0-7> (see details above), f 54;
#X text 213 444 - hermite interpolation bias (default 0), f 54;
#X text 213 460 - hermite interpolation tension (default 0), f 54;
#X text 213 396 - phase signal to read the array (values from 0-1);
#X text 176 634 @interp <f> (interpolation mode \, default 1: linear);
#X text 146 649 @interp_bias <f> (default 0) | @interp_tension <f> (default 0), f 63;
#X text 213 560 - array name (required), f 54;
#X text 213 611 - number of output channels (max 64) - default 1;
#X obj 166 224 output~;
#X obj 2 3 ./header wave~;
#X text 22 61 Wavetable reader;
#X obj 23 240 declare -stdpath ./;
#X obj 185 312 tabosc4~;
#X obj 185 352 tabread4~;
#X obj 185 332 tabread~;
#X obj 77 312 cyclone/cycle~;
#X obj 77 332 cyclone/lookup~;
#X obj 77 352 cyclone/play~;
#X text 10 333 see also:;
#X obj 464 345 open-else;
#X text 253 319 Plugdata users or those with ELSE can also use the more powerful [else/loop] as an alternative., f 33;
#X msg 464 317 wavetable~;
#X text 468 296 click:;
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