Foundation Knowledge Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation Confused Fact Finder Biased Jumper Perpetual Analyzer Pragmatic Performer Strategic Re-visioner Distinguish relevant & irrelevant Information Read conflicting opinions Relate assumptions & biases Analyze pros & cons Prioritize issues and information Justify assumptions Articulate vision Reinterpret information Steps for Better Thinking Performance Patterns, Developmental Framework for Critical Thinking ObservationInterpretation Judgment Planning Steps in Critical Thinking Performance Patterns Interventions Step 1Step 2Step 3Step 4

Computer – Sketch Recognition Foundation Knowledge: Stroke, Sezgin Method, Yu Method Which primitive (or group) is this stroke? Line, Arc, Ellipse Precedence, Error, Tolerance What about a Rubine gesture? Foundation Knowledge Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation ObservationInterpretation Judgment Planning

Computer – Sketch Recognition Foundation Knowledge: Stroke, Rubine Method, Sezgin Method, Yu Method Which primitive (or group) or gesture is this stroke? Line, Arc, Ellipse, RGesture1, RGesture2 Precedence, Error, Tolerance What about combination of strokes? May change lower level interpretations… geometric context Foundation Knowledge Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation ObservationInterpretation Judgment Planning

US Foundation Knowledge: Stroke, Sezgin Method, Yu Method Which primitive (or group) is this stroke? Line, Arc, Ellipse Precedence, Error, Tolerance What about a Rubine gesture? Foundation Knowledge Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation ObservationInterpretation Judgment Planning

Recognizing a Line Foundation Knowledge: Stroke, Sezgin Method, Yu Method, Geometry How do we find *line* tolerance & error Options: –Least-squares error from endpoints: + Uses endpoints - Endpoint tails not removed - Error may be larger than true error –Least-square error with best fit line: + Find best-fitting line - Doesn’t necessarily use perceptually important start & end points + Can remove non-perceptually important tails –feature area: + In theory, can be compared to other shapes - Confusing - Value not apparent ? Smaller range –ratio: euclidean length/stroke length: + Easy to calculate + Uses perceptually important start & end point - Endpoint tails not removed Doesn’t differentiate between one point being far away and several points being near - Bigger range so harder to figure out a good threshold –Least-squares error using best fit, but then use endpoints - Error not same as what is chosen + Error is more representative of line + Perceptually important endpoints Foundation Knowledge Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation ObservationInterpretation Judgment Planning

Recognizing an Arc Foundation Knowledge: –Method to find sample arc as part of a circle: Connect endpoints, find perpendicular bisector of that line Find where that line intersects stroke Make two lines connecting center stroke point and endpoints Find perpendicular bisector of each line Intersecting point is circle center Find feature area –A curve of order 2 Options: –Least-squares error from endpoints with a curve of order 2: + Uses endpoints + Easy to compute - Not actually an arc –Feature area + Uses real arc + Faster ? - Need the line of the arc, because takes the feature area - Difficult – polygons could be above or below Idea: Add threshold to radius – for comparing against line –Least squared error with arc itself + Uses real arc - Harder to compute + Faster? Compute distance of each point to the center – subtract from radius Foundation Knowledge Identify The Problem Explore Interpretations & Connections Prioritize Alternatives Envision Strategic Innovation ObservationInterpretation Judgment Planning

Recognizing a Circle Foundation Knowledge: –Method to find direction graph slope Direction graph: Find direction of each point –Direction vs. time since start »Depends on time since start –Direction vs. point number »Depends on sampling rate –Direction vs. stroke length »More time computationally Find slope Fit a line to direction graph – use same least square method –Splitting: Spilt it when change in direction (every) 2pi –Circle center: center of bounding box or average of all points –Circle radius: Bounding box / 2 Average distance from center Options: –Slope of the direction graph == 2pi/n Doesn’t handle tails Overtracing difficult because have to split –Direction graph is linear –Circle least squares –Circle feature area

Recognizing a Ellipse Foundation Knowledge: –Method to find direction graph slope Use endpoints Find best fit line of direction graph –Major axis and minor axis not equal –To find major axis Two points w/ greatest distance is the major axis –Perpendicular bisector is minor axis (where it intersects stroke) –Should points also intersect a calculated center point? Fit a line to the ellipse –To find center point Center of bounding box Center of longest line Center of mass –Area of Ellipse PI * (length of major axis/2) * (length of minor axis/2) –Definition of Ellipse Sum of the distance from focus 1 and focus 2 is constant X^2 / a^2 + y^2 / b^2 = 1 –A = ½ major axis, b = ½ minor axis Focal point is the point on the major axis that is distance ‘A’ from where minor axis intersects ellipse Options: –Slope of the direction graph ~2pi/n –Ellipse least squares – need foci –Ellipse feature area Small triangles to center vs actual ellipse area

Recognizing a Ellipse, Part 2 Length of Major Axis –Fit a line –Longest distance Length of Minor Axis –Rotate Ellipse to find height of BB –Average distance of stroke points that intersect minor axis from the major axis –Calculate from perimeter formula (p = strokelength = pi * sqrt(2*(s^2 + b^2) – (a-b)^2/2) –Calculate distance from every point to the major axis: Minor axis = average distance * pi / 2 –Eigenvector method –Closest point to center

Helix Recognition Find major, minor axis (rotated b b) Find number of rotations (direction graph from circle) Combine n helix components Rotate, scale and translate X = cos(t) + change in x at t Y = sin(t) + change in y at t