将x和y值映射到屏幕坐标

Question

如何将用户指定的x和y值（无论以何种比例）映射到 屏幕坐标？这就是Stata在生成图形时在内部执行的操作。

例如：

clear
set seed 1234567890
set obs 500

generate y = rnormal(434.80132, 237.89369)
generate x = rnormal(0.08, 0.04)

twoway scatter y x
classutil describe .Graph.plotregion1

    double       .drawn_yalpha  = 8238.730168
    double       .drawn_ybeta   = 9.137843887999999
    double       .drawn_xalpha  = 8797.446232487588
    double       .drawn_xbeta   = 102552.7601697518
    double       .drawn_gbeta   = 232.72

    double       .gdi_y0        = 3157.824224
    double       .gdi_x0        = 3157.824224
    double       .gdi_y1        = 22457.48
    double       .gdi_x1        = 31184.48

twoway scatter y x || function y = 7000*x, range(0 0.15)
classutil describe .Graph.plotregion1

    double       .drawn_yalpha  = 9787.283955999999
    double       .drawn_ybeta   = 8.105474695999998
    double       .drawn_xalpha  = 8797.446232487588
    double       .drawn_xbeta   = 102552.7601697518
    double       .drawn_gbeta   = 232.72

    double       .gdi_y0        = 5222.562608
    double       .gdi_x0        = 3157.824224
    double       .gdi_y1        = 22457.48
    double       .gdi_x1        = 31184.48

Stata的文档没有描述如何计算所有这些。