全方位抛物线

来源

Mosiv的语雀笔记：《全方位抛物线》

原文

x-y平面绕 x轴, 旋转30°得到旋转后平面p1, a点投影在p1平面,
其坐标Vector(x,y,z) (x,y为抛物线在2D平面坐标, z为抛物线高度), x不变, y变化
H = (z - (ytan30°)) * sin30°+ (y / cos30°)
得到变换后 a点 坐标 Vector( x , H )

代码：

extends Path2D
var trans_points :PoolVector2Array = []
var points :PoolVector2Array = []
# 抛物线平面方向
var dirction = Vector2.RIGHT
# 平面旋转角度
var plane_rotate_rad :float= -PI/3
var start_speed_vertical = 100
var speed_hotizontal = 20
var speed_vertical = start_speed_vertical
var gravity := -10.0
var timer := 0.0
var is_over := false
func _process(delta): 
  if is_over :return
  for i in range(8):
    caculate(dirction.rotated(PI/4 * i),delta)
# 计算位置
func caculate(direction,delta):
  timer += delta
  var vertical_heigt = start_speed_vertical*timer + (gravity * timer * timer )/2 
  var horizontal_position = direction * speed_hotizontal * timer 
  var trans_pos = trans(Vector3(horizontal_position.x,horizontal_position.y,vertical_heigt))
  trans_points.append(trans_pos)
  points.append(horizontal_position)
  update()
  if vertical_heigt  <= 0:
    is_over = true
    print("over")
# 绘制
func _draw():
  if points.size() < 2:return
    draw_polyline(points,Color.red,5.0)
    draw_polyline(trans_points,Color.chartreuse,5.0)
# 变换坐标
func trans(pos:Vector3)->Vector2:
  var x = pos.x
  var y = (pos.z - (pos.y*tan(plane_rotate_rad)))*sin(plane_rotate_rad) + (pos.y / cos(plane_rotate_rad))
    return Vector2(x,y)