---------------------------------------------------------------------- _The SICP Picture Language_ ---------------------------------------------------------------------- ---------------------------------------------------------------------- INTRODUCTION ---------------------------------------------------------------------- The SICP Picture Language is a small language for drawing pictures. It shows the power of data abstraction and closure. The picture language stems from Peter Henderson's 1982 paper "Functional Geometry" and was included by Hal Abelson in "Structure and Interpretation of Computer Programs". Before using this package, read section 2.2.4 of SICP, which is an excellent introduction to the ideas of the picture language. The documentation below is only meant as a quick reference guide. <http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-15.html#%_sec_2.2.4> Peter Henderson has written an updated version of "Functional Geometry", which explains how to construct the Escher fish image. <http://eprints.ecs.soton.ac.uk/7577/01/funcgeo2.pdf> ---------------------------------------------------------------------- REFERENCE ---------------------------------------------------------------------- The basic concept of the picture language is a _painter_. A painter draws it's image (shifted and scaled) within a frame given by a parallelogram. Painters can be combined to construct new painters. EXAMPLE ------- > (require (planet "picture.ss" ("soegaard" "sicp" 1 0))) > (paint (number->painter 0)) > (paint diagonal-shading) > (paint-hires (below (beside diagonal-shading (rotate90 diagonal-shading)) (beside (rotate270 diagonal-shading) (rotate180 diagonal-shading)))) > (paint einstein) VECTORS ------- An mathematical vector is called a vect here, in order to avoid confusion with the builtin vectors of Scheme. > make-vect : number number -> vect Construct a vect with the given coordinates. > vector-xcor : vect -> number Return the x-coordinate of the vect. > vector-ycor : vect -> number Return the y-coordinate of the vect. > vector-add : vect vect -> vect Add two vect by adding their coordinated pairwise. > vector-sub : vect vect -> vect Subtract two vects by subtracting their coordinated pairwise. > vector-scale : number vect -> vect Scale the vect by multiplying each coordinate with the number. FRAMES ------ A frame is descibed by three vectors. ^ | frame edge2 vector | _|__________> /| frame edge1 vector / / / frame origin pointer > make-frame : origin edge1 edge2 -> frame Construct a frame from a frame origin vector and two frame edge vectors. > frame-origin : frame -> vect > frame-edge1 : frame -> vect > frame-edge2 : frame -> vect Extracts the origin, first edge or second edge from a frame. > make-relative-frame : origin corner1 corner2 -> (frame -> frame) The procedure make-relative-frame provides a convenient way to transform frames. Given a frame and three points : origin, corner1, and corner2 (expressed in frame coordinates), it returns a new frame with those corners. > frame-coord-map : frame -> (vect -> vect) Each frame determines a system of "frame coordinates" (x,y) where (0,0) is the origin of the frame, x represents the displacement along the first edge (as a fraction of the length of the edge) and y is the displacement along the second edge. The frame coordinate map is returned by frame-coord-map. E.g these expression return the same value: ((frame-coord-map a-frame) (make-vect 0 0)) (frame-origin a-frame) SEGMENTS -------- A pair of vectors determines a directed line segment - the segment running from the endpoint of the first vector to the endpoint of the second vector. > make-segment : vect vect -> segment > segment-start : segment -> vect > segment-end : segment -> vect PRIMITIVE PAINTERS ------------------ Painters take a frame and draw an image, transformed to fit inside the frame. There are four ways to create painters: 1) from a constant: number->painter 2) from a list of line segments: segment->painter 3) form a procedure: procedure->painter 4) from a picture: picture->painter > number->painter : 0..255 -> painter Construct a painter that fills the frame with a gray color indicated by the number. 0 is black and 255 is white. > segments->painter : list-of-segment -> painter Construct a painter that draws a stick figure given by the segments (wrt the unit square). > procedure->painter : procedure -> painter Creating painters from procedures. We assume that the procedure f is defined on the unit square. Then to plot a point p in the target frame, we find the inverse image T^-1(p) of p under the transformation that maps the unit square to the target, and find the value of f at T-1(p). > picture->painter : picture -> painter The picture p is defined on some frame. Given a point p in the target frame, we compute T^-1(p) where T is the transformation that takes the picture frame to the target frame, and find the picture value at the closest integer point. > load-painter : file-name -> painter Uses the picture in file-name to create a painter. HIGHER ORDER PAINTERS --------------------- > transform-painter : origin corner1 corner2 -> (painter -> painter) A painter can be transformed to produce a new painter which, when given a frame, calls the original painter on the transformed frame. Transform-painter will given an origin and two corners, return a function that takes a painter as argument and returns a transformed painter. > flip-horiz : painter -> painter Returns a painter that flips the image horizontally. > flip-vert : painter -> painter Returns a painter that flips the image vertically. > rotate90 : painter -> painter > rotate180 : painter -> painter > rotate270 : painter -> painter Returns a painter that totates the image. > beside : painter painter -> painter Constructs a painter that paints the images side-by-side. > below : painter painter -> painter Constructs a painter that paints the second image below the first. > superpose : painter painter -> painter Constructs a painter that paints the two images on top of each other. SIMPLE BUILTIN PAINTERS ----------------------- The following painter values are buitin: black, white and gray Fills the frame with black (0), white (255) or gray (150). diagonal-shading Fills the frame with a shades of gray. The color transition goes from black in the upper left corner is black, to gray in the bottom right corner. einstein Draws an image of Einstein. PAINTING -------- The procedures paint and paint-hi-res takes a painter as input and return a snip containing the painter's image. A snip is an image that DrScheme can display automatically. > paint : painter -> snip > paint-hi-res : painter -> snip ---------------------------------------------------------------------- AUTHORS ---------------------------------------------------------------------- Abelson & Sussman: <http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-15.html#%_sec_2.2.4> Daniel Coore: Original MIT Scheme code Mike Sperber: PLT port Jens Axel Søgaard: Documentation ---------------------------------------------------------------------- OTHER ---------------------------------------------------------------------- See also <http://mitpress.mit.edu/sicp/psets/ps4hnd/readme.html> for more documentation and exercises. Peter Henderson's "Functional Geometry": <http://eprints.ecs.soton.ac.uk/7577/01/funcgeo2.pdf> Keywords: _SICP_ _sicp_ _painter_ _geometry_ _picture_ _Escher_