Dev:Potential Formula Framework - Revision history

Jose X: some more reworkings

2010-05-31T06:02:53Z

some more reworkings

Jose X at 04:17, 31 May 2010

2010-05-31T04:17:51Z

Jose X: Some more reworkings

2010-05-31T04:14:49Z

Some more reworkings

Jose X: some more reworkings

2010-05-31T04:05:29Z

some more reworkings

Jose X at 02:39, 31 May 2010

2010-05-31T02:39:30Z

Jose X: /* Creating and Editing Formulas through the Formula Panel */

2010-05-31T02:35:42Z

‎Creating and Editing Formulas through the Formula Panel

Jose X: /* Graphical Formula Support */

2010-05-31T02:27:22Z

‎Graphical Formula Support

Jose X: /* Animations Present Challenges */

2010-05-31T02:11:40Z

‎Animations Present Challenges

Jose X: /* Formulas in the World of Animations */

2010-05-31T02:06:55Z

‎Formulas in the World of Animations

Jose X: /* Introduction */

2010-05-31T02:04:07Z

‎Introduction

@@ Line 31: / Line 31: @@
 As an example [add table diagram later], a table with rows: "1", "34.3"; "2", "23"; and "3", "235"; represents that the parameter has value 34.3 for frame 1, 23 for frame 2, and 235 for frame 3.
-fgdfgdf
+[In this and other early sections of this page, we'll use formula string notation that might be a bit simplified from the full string syntax described later.]
-[In the next section, we'll overview an example notation that can capture this information in a fairly compact fashion.]
 In the most general form, at each row we can represent the value of the parameter as a formula that applies only at that frame. And each row can have a different formula. This general case is where each frame's value is defined very differently from each other for that parameter. [Note, that a value is a special case of a formula, eg, y=5 is a value and a formula.. and so is y=sin(x) @ x=6]
@@ Line 69: / Line 69: @@
 { 3sin( { x, [6, 66-67, 73]:x+1, [7]:2x+1} ), [9]:4sin(x), [15]:47 }
 == Formula String Syntax in More Detail ==
@@ Line 89: / Line 93: @@
 === Full BNF ===
 == Some Issues not yet Addressed ==

← Older revision		Revision as of 04:17, 31 May 2010
Line 85:		Line 85:

	==== Example of Formula String that Includes Parameter Linking ====		==== Example of Formula String that Includes Parameter Linking ====
		+
		+	=== Example of Formula String and the Corresponding SIF sections ===

	=== Full BNF ===		=== Full BNF ===

@@ Line 48: / Line 48: @@
 Eg, if every single frame can be described through some version of a sine wave, then we might define the full correct mapping (taking waypoints into account) from some version of a sine wave with `{' `}' within the formula to specify parts that vary according to the table.
-== Example 1 of Formula String with Waypoints ==
+=== Example 1 of Formula String with Waypoints ===
 If the first through fifth frames have value 3sin(x), the sixth frame has value 3sin(x+1), the seventh frame has value 3sin(2x+1), and the eigth through 100th frames have 3sin(x), then the full mapping can be described by:
@@ Line 62: / Line 62: @@
 Well, starting with a (canonical) tree representation of 3sin(x) [pic goes here], we find that that same tree lasts throughout the entire 100 frames, except that the node initially holding x gets replaced (with x+1, later with 2x+1, and then again with x). Thus, we can represent the full mapping by a formula representing the constant outside parts and one or more internal tables { } to capture the parts that did vary within the tree. If the function had changed at the root level, then our mapping would be an outer level bifurcation (more than one formula template) so as to capture all 100 rows within at least one of the bifurcation parts. Remember that the general form for any mapping for a parameter during 100 frames would be a 100 row table. [In our current case, all of those 100 rows have "3sin (blah)".]
-== Example 2 of Formula String with Waypoints ==
+=== Example 2 of Formula String with Waypoints ===
 As above but row 9 is defined by 4sin(x), row 15 by 47, and rows 66, 67, and 73 by 3sin(x+1).
@@ Line 70: / Line 70: @@
 { 3sin( { x, [6, 66-67, 73]:x+1, [7]:2x+1} ), [9]:4sin(x), [15]:47 }
-== Example of Formula String that Includes Parameter Linking and Shows the Automatically Generated Synfig Conversions ==
+== Formula String Syntax in More Detail ==
 == Some Issues not yet Addressed ==
@@ Line 96: / Line 112: @@
 A Formula Neighbor Panel is like a Formula Panel except that it is independent of whatever layer parameter may happen to be selected at that point in time (ie, it's decoupled from current selections).
 === Creating and Editing Formulas through the Formula Panel ===
 [Eventually, there will be mock pictures to show all the features of formula creation/editing in action.]
 ==== An Example ====

@@ Line 17: / Line 17: @@
 == Animations Present Challenges ==
-Currently, determining the value a parameter takes at some point in time is achieved either (a) by setting the value of the parameter to a constant value (for all frames), either (a1) directly or (a2) after having introduced {{l|Convert|conversions}} and linking, (b) by setting the value of the parameter to a different value in at least two frames (ie, introducing one or more dependent waypoints), using {{l|Doc:Animation Basics|"Animate Editing Mode"}} or introducing the {{l|Convert#Linear|conversion frame dependency}}, either (b1) directly or (b2) after having introduced conversions and linking, or (c) through the process of interpolation that takes effect for frames being animated between relevant waypoints, either (c1) directly or (c2) after having introduced conversions and linking at either of the adjacent waypoints. ["Directly" means the parameter's value has no conversions or linking.]
+Currently, determining the value a parameter takes at some point in time is achieved either (a) by setting the value of the parameter to a constant value (for all frames), either (a1) directly or (a2) after having introduced {{l|Convert|conversions}} and linking; (b) by setting the value of the parameter to a different value in at least two frames (ie, introducing one or more dependent waypoints), using {{l|Doc:Animation Basics|"Animate Editing Mode"}} or introducing the {{l|Convert#Linear|conversion frame dependency}}, either (b1) directly or (b2) after having introduced conversions and linking; or (c) through the process of interpolation that takes effect for frames being animated between relevant waypoints, either (c1) directly or (c2) after having introduced conversions and linking at either of the adjacent waypoints. ["Directly" means the parameter's value has no conversions or linking.]
 The motivation behind introducing a formula framework is to provide a simpler interface to the current procedure used to create conversions ((a2), (b2), (c2)). As a special case, setting the value of a parameter "directly" ((a1), (b1), (c1)) also falls within the scope of a formula, namely the formula "= c", where c is the direct constant value chosen.
@@ Line 23: / Line 23: @@
 For cases (b) and (c), where waypoint dependencies have been introduced, a "simple" explicit formula is not likely to describe the parameter's value at all frames. We would likely need multiple formulas, each applying to the disjoint subsets of a [http://en.wikipedia.org/wiki/Partition_of_a_set partitioning] of all the frames.
-To see how we might be able to deal with the effects of the waypoints, we consider that a function (in the mathematical sense) is nothing but a mapping from one set of values to another set of values. In our case here, we have a mapping from the set of frame numbers (ie, the natural numbers, 1, 2, 3, .. up to the last frame number) to the set of values the given parameter will take at each frame (eg, a real value). That is, we want a "formula" to specify what single value the parameter will take at each individual frame. A single simple formula won't be correct, in general, amid animation waypoints and the associated interpolations. We'll need a bifurcation consisting of multiple formulas.
+To see how we might be able to deal with the effects of the waypoints, we consider that a function (in the mathematical sense) is nothing but a mapping from one set of values to another set of values. In our case here, we have a mapping from the set of frame numbers (ie, the natural numbers, 1, 2, 3, .. up to the last frame number) to the set of values the given parameter will take at each frame (eg, a real value). That is, we want a "formula" to specify what single value the parameter will take at each individual frame. A single simple formula won't be correct, in general, amid animation waypoints and the associated interpolations. We'll need a bifurcation consisting of multiple formulas with supporting notation.
-We can represent any mapping (ie, "formula") as a two column table. This is the most general way to specify our formulas. The rows are labeled 1, 2, 3... (representing each frame) as the value within column one, and the value in the second column at a given row is the value the parameter takes at the frame number (at the column one value).
+== Formulas that Capture All Frame Values despite Animations ==
-As an example, a table with rows: "1", "34.3"; "2", "23"; and "3", "235"; represents that the parameter has value 34.3 for frame 1, 23 for frame 2, and 235 for frame 3.
+We can represent any mapping (ie, "formula") as a two column table. This is the most general way to specify our mappings. The rows are labeled 1, 2, 3 in column one (to represent each frame), and the value in the second column is the value the parameter takes at that frame number.
-[In the next section, we'll overview an example notation that can capture this information in a fairly compact fashion.]
+As an example [add table diagram later], a table with rows: "1", "34.3"; "2", "23"; and "3", "235"; represents that the parameter has value 34.3 for frame 1, 23 for frame 2, and 235 for frame 3.
-== Formulas that Capture All Frame Values despite Animations ==
+fgdfgdf
 In the most general form, at each row we can represent the value of the parameter as a formula that applies only at that frame. And each row can have a different formula. This general case is where each frame's value is defined very differently from each other for that parameter. [Note, that a value is a special case of a formula, eg, y=5 is a value and a formula.. and so is y=sin(x) @ x=6]

← Older revision		Revision as of 02:39, 31 May 2010
Line 68:		Line 68:

	{ 3sin( { x, [6, 66-67, 73]:x+1, [7]:2x+1} ), [9]:4sin(x), [15]:47 }		{ 3sin( { x, [6, 66-67, 73]:x+1, [7]:2x+1} ), [9]:4sin(x), [15]:47 }
		+
		+	== Example of Formula String that Includes Parameter Linking and Shows the Automatically Generated Synfig Conversions ==

	== Some Issues not yet Addressed ==		== Some Issues not yet Addressed ==

← Older revision		Revision as of 02:35, 31 May 2010
Line 95:		Line 95:

	=== Creating and Editing Formulas through the Formula Panel ===		=== Creating and Editing Formulas through the Formula Panel ===
		+
		+	[Eventually, there will be mock pictures to show all the features of formula creation/editing in action.]
		+
		+	==== What Does the Formula Panel Look like? ====
		+
		+	==== An Example ====
		+
		+	Let's see how we can create graphically the following formula: { []:3sin(2x+4), []: }

	fghfghfghg		fghfghfghg

@@ Line 84: / Line 84: @@
 == Graphical Formula Support ==
-A Formula Panel would show the existing formula (as per the above notation) for a selected parameter or more than one parameter if they match (maybe even try to factor out the common portions if multiple parameters have been selected).
+=== The Formula Panel ===
-A Formula Tool (or the Formula Panel) would be used to create and edit formulas. You drag and drop any of various well-defined formula components (like sin(x) or +). This would roughly pattern the conversions possible in synfig today. There would be a way to explicitly add row exceptions: "{ ... }". The location of the drop would define how the component modified the existing partial formula being created. Instead of adding further formula components at extension points (perhaps represented by variables initially.. and representing the parameters of the related synfig conversion), we can define these as a constant value or link to another parameter.
+A Formula Panel shows the value of a selected layer parameter using the formula system described on this page.
 The formula creation GUI might have multiple views since some might be preferable over others depending on context and the synfig user.

@@ Line 3: / Line 3: @@
 == Introduction ==
-We aim to associate a function definition (ie, a formula) with any given parameter (of a layer). The compact syntax of the typical mathematical notation could be an efficient way to represent the value of a parameter across all frames.
+We aim to define layer parameters through a function definition (ie, a formula). The compact syntax of the typical mathematical notation could be an efficient way to represent the value of a parameter across all frames.
-In its most flexible form, conversions and linking require a significant amount of manual work subject to error and resulting in a nontrivial loss of time. We want to substitute the conversion and linking with the specification of formulas.
+Today, creating synfig conversions (potentially with linking) can require a significant amount of manual work subject to error and resulting in a nontrivial loss of time. [As an example, see {{l|Parabolic Shot|this tutorial}}.] We want to substitute the manual conversion procedure with the specification of formulas.
-We understand that a single compact formula may very likely cease to represent the value of the parameter once we have introduced animations. Our "formula" must include all information necessary to account for any possible change over time (ie, over frames).
+We understand that a single compact formula may very likely cease to represent the value of the parameter once we have introduced animations. Our formula system must then include all information necessary to account for any possible change over time (ie, over frames), and, since animations can introduce rather arbitrary changes in value, this can potentially lead to a very complex specification of our formula.
-We'd like a string representation of a "formula". We'd like a graphical interface for creating and manipulating a formula.
+We'd like each "formula" to have a string representation that is as simple as possible.
 We also want to be able to go back and forth between the sif representation of the value for a parameter and the formula form.