divert(-1)
changecom(`%')

% SQUAREANGLE(point, dir_point1, dir_point2, prefix)
% Draws a square angle mark at 'point', with sides pointing to
% 'dir_point1' and 'dir_point2'. 'prefix' must be a unique string.
define(`SQUAREANGLE',
	`% square angle sign
	def $4a sqsz * unit($2-$1)
	def $4b sqsz * unit($3-$1)
	def P$4`'1 $1+[$4a]
	def P$4`'2 $1+[$4a]+[$4b]
	def P$4`'3 $1+[$4b]
	line(P$4`'1)(P$4`'2)(P$4`'3)')


% ARCANGLE(point, dir_point1, dir_point2, prefix, radius, cfac)
% Draws an angle arc mark at 'point', with sides pointing from
% 'dir_point1' to 'dir_point2'. 'prefix' must be a unique string.
% 'radius' is the arc radius. 'cfac' is a spline control point
% distance factor (experiment with it).
define(`ARCANGLE',
	`% angle arc
	def $4a unit($2-$1)
	def $4b unit($3-$1)
	def $4c [$4b] - [$4a] * ([$4a] . [$4b])
	def $4d [$4a] - [$4b] * ([$4a] . [$4b])
	def $4Pa $1 + $5 * [$4a]
	def $4Pb $1 + $5 * [$4b]
	def $4Pc ($4Pa) + $6 * [$4c]
	def $4Pd ($4Pb) + $6 * [$4d]
	def $4Pmid $1 + $5 * unit([$4a]+[$4b])
	special |\draw[->] #1 .. controls #2 and #3 .. #4;|
		($4Pa)($4Pc)($4Pd)($4Pb)')
divert(0)dnl

def axn -0.4
def axp 0.9
def sqsz 0.1
def P (0.8,-1.0,0.7)
def O (0,0,0)

def axes {
	line[arrows=->](axn,0,0)(axp,0,0)
	line[arrows=->](0,axn,0)(0,axp,0)
	line[arrows=->](0,0,axn)(0,0,axp)
	special |\node[anchor=east] at #1 {$x$};| (axp,0,0)
	special |\node[anchor=west] at #1 {$y$};| (0,axp,0)
	special |\node[anchor=north] at #1 {$z$};| (0,0,axp)
}

def pict {
	line[arrows=->,line width=1.0pt](0,0,0)(P)
	special |\node[anchor=east] at #1 {$\vec{v}$};|(P)

	def Pxz scale([1,0,1]) * (P)
	def Pz scale([0,0,1]) * (P)
	def Px scale([1,0,0]) * (P)
	line[line style=dotted](P)(Pxz)
	line[line style=dotted](0,0,0)(Pxz)
	line[line style=dotted](Pxz)(Pz)
	line[line style=dotted](Pxz)(Px)

	SQUAREANGLE((Pz),(Pxz),(O),a)
	SQUAREANGLE((Px),(Pxz),(O),e)
	SQUAREANGLE((Pxz),(P),(O),b)

	ARCANGLE((O),(0,0,1),(Pxz),c,0.4,0.15)
	special |\node[anchor=west] at #1 {$\theta$};|(cPmid)

	ARCANGLE((O),(Pxz),(P),d,0.3,0.1)
	special |\node[anchor=west] at #1 {$\phi$};|(dPb)
}

def off -10
def pers 20
def eye (pers,off,5)
def lookat (0,off,5)
def up [0,-1,0]
put { view((eye),(lookat), [up]) then perspective(pers*3) } {
	{axes}
	{pict}
}

global {
	language tikz
}