submodule "point.pli"
submodule "vector.pli"
submodule "functions.pli"
module "matrix.pli"
type MorphMatrix
field Float xx xy xt
field Float yx yy yt
function build m
arg_w MorphMatrix m
m xx := 1 ; m xy := 0 ; m xt := 0
m yx := 0 ; m yy := 1 ; m yt := 0
function morph sx sy rx ry tx ty -> m
arg Float sx sy rx ry tx ty ; arg MorphMatrix m
m xx := sx*cos:rx
m xy := -sy*sin:ry
m xt := tx
m yx := sx*sin:rx
m yy := sy*cos:ry
m yt:= ty
method mo matrix -> ma
arg MorphMatrix mo ; arg Matrix ma
ma resize 3 3
ma 0 0 := mo xx
ma 0 1 := mo xy
ma 0 2 := mo xt
ma 1 0 := mo yx
ma 1 1 := mo yy
ma 1 2 := mo yt
ma 2 0 := 0
ma 2 1 := 0
ma 2 2 := 1
function morph ma -> mo
arg Matrix ma ; arg MorphMatrix mo
check ma:nb_lines=3 and ma:nb_columns=3
mo xx := ma 0 0
mo xy := ma 0 1
mo xt := ma 0 2
mo yx := ma 1 0
mo yy := ma 1 1
mo yt := ma 1 2
function compose mo1 mo2 -> mo
arg MorphMatrix mo1 mo2 mo
mo := morph mo2:matrix*mo1:matrix
function compose mo1 mo2 mo3 -> mo
arg MorphMatrix mo1 mo2 mo3 mo
mo := morph mo3:matrix*mo2:matrix*mo1:matrix
function reverse mo -> inv
arg MorphMatrix mo inv
inv := morph mo:matrix^(-1)
method m '' p -> q
arg MorphMatrix m ; arg Point2 p q
q := point p:x*m:xx+p:y*m:xy+m:xt p:x*m:yx+p:y*m:yy+m:yt
method m '' v -> w
arg MorphMatrix m ; arg Vector2 v w
w := vector v:x*m:xx+v:y*m:xy v:x*m:yx+v:y*m:yy
export MorphMatrix morph '' '. matrix' compose reverse
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