创建一个函数，使线段坐标以点 (x y) 为中心，斜率为 m

Question

我正在构建一个绘图库 source，我想绘制斜线。我有一个函数 (draw-seg-list device color lst)，其中 lst arg 是一个列表，其中包含带有一行 (x0 y0 x1 y1) 的开始和停止线的列表。我想创建一个函数 (make-slope-seg x y m) 然后 returns 以 (x, y) 为中心、斜率为 m 的线段的点列表。

示例：(make-slope-seg 0 0 0) -> (-.05 0 .05 0) 和 (make-slope-seg .1 .1 1) -> (.05 .05 .15 .15)

我的非工作函数是：

(define (make-slope-cords x y m)
  (list (- x .05)
        (* y m -1)
        (+ x .05)
        (* y m)))

其中 returns 行不正确。如果我使用：

;makes graphics window
(define window (make-graphics-device 'win32))

;plots blue line for function y = x^2 with black axis
(make-plot window 'simple-plot (list "white" "black" "blue" (list (range -1 1 .01) square)))

;makes list of lists containing the slope and x y cords that the slope lines
;are supposed to be centered at
(define cords (map (lambda (s x y)
                     (list s x y))
                   (map (lambda (x) (* 2 x)) (range -1 1 .1))
                   (range -1 1 .1)
                   (map square (range -1 1 .1))))

;plots the line segments generated by mapping make-slope-cords to the coordinate list
(draw-seg-list window "red"
               (map (lambda (lst)
                      (make-slope-cords (car lst) (cadr lst) (caddr lst)))
                    cords))

输出如下：

但我希望它输出宽度为 .1 的红线（图像中网格上的 1 个正方形），斜率是蓝线的斜率（lambda (x) (square x)) 在每个点间隔沿 x 轴 .1。

注意：假设 draw-seg-list 有效。我只需要帮助使函数 make-slope-cords 生成正确的坐标列表

Answer 1

经过反复试验，我确定了答案。

(define (make-sloped-seg x y m)
  (define b (- y (* m x)))
  (list (- x .03)
        (+ (* m (- x .03)) b)
        (+ x .03)
        (+ (* m (+ x .03)) b)))

它在计算开始时确定y轴截距(b)，然后使用正确的截距生成点

示例：

;makes graphics window
(define window (make-graphics-device 'win32))

;plots blue line for function y = x^2 with black axis
(make-plot window 'simple-plot (list "white" "black" "blue" (list (range -1 1 .01) square)))

;makes list of lists containing the slope and x y cords that the slope lines
;are supposed to be centered at
(define cords (map (lambda (s x y)
                     (list s x y))
                   (map (lambda (x) (* 2 x)) (range -1 1 .1))
                   (range -1 1 .1)
                   (map square (range -1 1 .1))))

;plots the line segments generated by mapping make-slope-cords to the coordinate list
(draw-seg-list window "red"
               (map (lambda (lst)
                      (make-slope-cords (car lst) (cadr lst) (caddr lst)))
                    cords))

输出如下：

创建一个函数，使线段坐标以点 (x y) 为中心，斜率为 m

Make a function that makes line segment coordinates centered at point (x y) with slope m

scheme

mit-scheme