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harmishhk/ linear_angular_velocity_relation.jl

Last active August 29, 2015 14:26
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linear_angular_velocity_relation.jl
using Gadfly
using Cairo
max_wheel_vel = 1.6
wheel_base = 0.78
calc_step = 0.01
arcs = Array(Float64, 0, 2)
data = Array(Float64, 0, 2)
r = wheel_base / 2
max_ang_vel = max_wheel_vel / r
for ang = -max_ang_vel:calc_step:max_ang_vel
for lin = 0:calc_step:(max_wheel_vel+calc_step)
vr = lin - r * ang
vl = lin + r * ang
if (abs(vr) > max_wheel_vel || abs(vl) > max_wheel_vel)
data = vcat(data, [lin ang])
arcs = vcat(arcs, [lin*cos(ang) lin*sin(ang)])
break
end
end
end
draw(SVGJS("dynamic-window.svg", 40cm, 16cm), plot(x=data[:,2], y=data[:,1], Geom.path()))
draw(SVGJS("possible-trajectories.svg", 30cm, 30cm), plot(x=arcs[:,2], y=arcs[:,1], Geom.path()))
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possible-trajectories.svg
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.selectAll("path")
.animate({stroke: destcolor}, 250);
// reveal zoom slider
root.select(".zoomslider")
.animate({opacity: 1.0}, 250);
};
// Unemphasize grid lines on mouse out.
Gadfly.plot_mouseout = function(event) {
var root = this.plotroot();
var xgridlines = root.select(".xgridlines"),
ygridlines = root.select(".ygridlines");
var destcolor = root.data("unfocused_xgrid_color");
xgridlines.attribute("stroke-dasharray", xgridlines.data("unfocused_strokedash"))
.selectAll("path")
.animate({stroke: destcolor}, 250);
destcolor = root.data("unfocused_ygrid_color");
ygridlines.attribute("stroke-dasharray", ygridlines.data("unfocused_strokedash"))
.selectAll("path")
.animate({stroke: destcolor}, 250);
// hide zoom slider
root.select(".zoomslider")
.animate({opacity: 0.0}, 250);
};
var set_geometry_transform = function(root, tx, ty, scale) {
var xscalable = root.hasClass("xscalable"),
yscalable = root.hasClass("yscalable");
var old_scale = root.data("scale");
var xscale = xscalable ? scale : 1.0,
yscale = yscalable ? scale : 1.0;
tx = xscalable ? tx : 0.0;
ty = yscalable ? ty : 0.0;
var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);
root.selectAll(".geometry, image")
.forEach(function (element, i) {
element.transform(t);
});
bounds = root.plotbounds();
if (yscalable) {
var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);
root.selectAll(".xfixed")
.forEach(function (element, i) {
element.transform(xfixed_t);
});
root.select(".ylabels")
.transform(xfixed_t)
.selectAll("text")
.forEach(function (element, i) {
if (element.attribute("gadfly:inscale") == "true") {
var cx = element.asPX("x"),
cy = element.asPX("y");
var st = element.data("static_transform");
unscale_t = new Snap.Matrix();
unscale_t.scale(1, 1/scale, cx, cy).add(st);
element.transform(unscale_t);
var y = cy * scale + ty;
element.attr("visibility",
bounds.y0 <= y && y <= bounds.y1 ? "visible" : "hidden");
}
});
}
if (xscalable) {
var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);
var xtrans = new Snap.Matrix().translate(tx, 0);
root.selectAll(".yfixed")
.forEach(function (element, i) {
element.transform(yfixed_t);
});
root.select(".xlabels")
.transform(yfixed_t)
.selectAll("text")
.forEach(function (element, i) {
if (element.attribute("gadfly:inscale") == "true") {
var cx = element.asPX("x"),
cy = element.asPX("y");
var st = element.data("static_transform");
unscale_t = new Snap.Matrix();
unscale_t.scale(1/scale, 1, cx, cy).add(st);
element.transform(unscale_t);
var x = cx * scale + tx;
element.attr("visibility",
bounds.x0 <= x && x <= bounds.x1 ? "visible" : "hidden");
}
});
}
// we must unscale anything that is scale invariance: widths, raiduses, etc.
var size_attribs = ["font-size"];
var unscaled_selection = ".geometry, .geometry *";
if (xscalable) {
size_attribs.push("rx");
unscaled_selection += ", .xgridlines";
}
if (yscalable) {
size_attribs.push("ry");
unscaled_selection += ", .ygridlines";
}
root.selectAll(unscaled_selection)
.forEach(function (element, i) {
// circle need special help
if (element.node.nodeName == "circle") {
var cx = element.attribute("cx"),
cy = element.attribute("cy");
unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,
cx, cy);
element.transform(unscale_t);
return;
}
for (i in size_attribs) {
var key = size_attribs[i];
var val = parseFloat(element.attribute(key));
if (val !== undefined && val != 0 && !isNaN(val)) {
element.attribute(key, val * old_scale / scale);
}
}
});
};
// Find the most appropriate tick scale and update label visibility.
var update_tickscale = function(root, scale, axis) {
if (!root.hasClass(axis + "scalable")) return;
var tickscales = root.data(axis + "tickscales");
var best_tickscale = 1.0;
var best_tickscale_dist = Infinity;
for (tickscale in tickscales) {
var dist = Math.abs(Math.log(tickscale) - Math.log(scale));
if (dist < best_tickscale_dist) {
best_tickscale_dist = dist;
best_tickscale = tickscale;
}
}
if (best_tickscale != root.data(axis + "tickscale")) {
root.data(axis + "tickscale", best_tickscale);
var mark_inscale_gridlines = function (element, i) {
var inscale = element.attr("gadfly:scale") == best_tickscale;
element.attribute("gadfly:inscale", inscale);
element.attr("visibility", inscale ? "visible" : "hidden");
};
var mark_inscale_labels = function (element, i) {
var inscale = element.attr("gadfly:scale") == best_tickscale;
element.attribute("gadfly:inscale", inscale);
element.attr("visibility", inscale ? "visible" : "hidden");
};
root.select("." + axis + "gridlines").selectAll("path").forEach(mark_inscale_gridlines);
root.select("." + axis + "labels").selectAll("text").forEach(mark_inscale_labels);
}
};
var set_plot_pan_zoom = function(root, tx, ty, scale) {
var old_scale = root.data("scale");
var bounds = root.plotbounds();
var width = bounds.x1 - bounds.x0,
height = bounds.y1 - bounds.y0;
// compute the viewport derived from tx, ty, and scale
var x_min = -width * scale - (scale * width - width),
x_max = width * scale,
y_min = -height * scale - (scale * height - height),
y_max = height * scale;
var x0 = bounds.x0 - scale * bounds.x0,
y0 = bounds.y0 - scale * bounds.y0;
var tx = Math.max(Math.min(tx - x0, x_max), x_min),
ty = Math.max(Math.min(ty - y0, y_max), y_min);
tx += x0;
ty += y0;
// when the scale change, we may need to alter which set of
// ticks is being displayed
if (scale != old_scale) {
update_tickscale(root, scale, "x");
update_tickscale(root, scale, "y");
}
set_geometry_transform(root, tx, ty, scale);
root.data("scale", scale);
root.data("tx", tx);
root.data("ty", ty);
};
var scale_centered_translation = function(root, scale) {
var bounds = root.plotbounds();
var width = bounds.x1 - bounds.x0,
height = bounds.y1 - bounds.y0;
var tx0 = root.data("tx"),
ty0 = root.data("ty");
var scale0 = root.data("scale");
// how off from center the current view is
var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),
yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);
// rescale offsets
xoff = xoff * scale / scale0;
yoff = yoff * scale / scale0;
// adjust for the panel position being scaled
var x_edge_adjust = bounds.x0 * (1 - scale),
y_edge_adjust = bounds.y0 * (1 - scale);
return {
x: xoff + x_edge_adjust + (width - width * scale) / 2,
y: yoff + y_edge_adjust + (height - height * scale) / 2
};
};
// Initialize data for panning zooming if it isn't already.
var init_pan_zoom = function(root) {
if (root.data("zoompan-ready")) {
return;
}
// The non-scaling-stroke trick. Rather than try to correct for the
// stroke-width when zooming, we force it to a fixed value.
var px_per_mm = root.node.getCTM().a;
// Drag events report deltas in pixels, which we'd like to convert to
// millimeters.
root.data("px_per_mm", px_per_mm);
root.selectAll("path")
.forEach(function (element, i) {
sw = element.asPX("stroke-width") * px_per_mm;
if (sw > 0) {
element.attribute("stroke-width", sw);
element.attribute("vector-effect", "non-scaling-stroke");
}
});
// Store ticks labels original tranformation
root.selectAll(".xlabels > text, .ylabels > text")
.forEach(function (element, i) {
var lm = element.transform().localMatrix;
element.data("static_transform",
new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));
});
var xgridlines = root.select(".xgridlines");
var ygridlines = root.select(".ygridlines");
var xlabels = root.select(".xlabels");
var ylabels = root.select(".ylabels");
if (root.data("tx") === undefined) root.data("tx", 0);
if (root.data("ty") === undefined) root.data("ty", 0);
if (root.data("scale") === undefined) root.data("scale", 1.0);
if (root.data("xtickscales") === undefined) {
// index all the tick scales that are listed
var xtickscales = {};
var ytickscales = {};
var add_x_tick_scales = function (element, i) {
xtickscales[element.attribute("gadfly:scale")] = true;
};
var add_y_tick_scales = function (element, i) {
ytickscales[element.attribute("gadfly:scale")] = true;
};
if (xgridlines) xgridlines.selectAll("path").forEach(add_x_tick_scales);
if (ygridlines) ygridlines.selectAll("path").forEach(add_y_tick_scales);
if (xlabels) xlabels.selectAll("text").forEach(add_x_tick_scales);
if (ylabels) ylabels.selectAll("text").forEach(add_y_tick_scales);
root.data("xtickscales", xtickscales);
root.data("ytickscales", ytickscales);
root.data("xtickscale", 1.0);
}
var min_scale = 1.0, max_scale = 1.0;
for (scale in xtickscales) {
min_scale = Math.min(min_scale, scale);
max_scale = Math.max(max_scale, scale);
}
for (scale in ytickscales) {
min_scale = Math.min(min_scale, scale);
max_scale = Math.max(max_scale, scale);
}
root.data("min_scale", min_scale);
root.data("max_scale", max_scale);
// store the original positions of labels
if (xlabels) {
xlabels.selectAll("text")
.forEach(function (element, i) {
element.data("x", element.asPX("x"));
});
}
if (ylabels) {
ylabels.selectAll("text")
.forEach(function (element, i) {
element.data("y", element.asPX("y"));
});
}
// mark grid lines and ticks as in or out of scale.
var mark_inscale = function (element, i) {
element.attribute("gadfly:inscale", element.attribute("gadfly:scale") == 1.0);
};
if (xgridlines) xgridlines.selectAll("path").forEach(mark_inscale);
if (ygridlines) ygridlines.selectAll("path").forEach(mark_inscale);
if (xlabels) xlabels.selectAll("text").forEach(mark_inscale);
if (ylabels) ylabels.selectAll("text").forEach(mark_inscale);
// figure out the upper ond lower bounds on panning using the maximum
// and minum grid lines
var bounds = root.plotbounds();
var pan_bounds = {
x0: 0.0,
y0: 0.0,
x1: 0.0,
y1: 0.0
};
if (xgridlines) {
xgridlines
.selectAll("path")
.forEach(function (element, i) {
if (element.attribute("gadfly:inscale") == "true") {
var bbox = element.node.getBBox();
if (bounds.x1 - bbox.x < pan_bounds.x0) {
pan_bounds.x0 = bounds.x1 - bbox.x;
}
if (bounds.x0 - bbox.x > pan_bounds.x1) {
pan_bounds.x1 = bounds.x0 - bbox.x;
}
element.attr("visibility", "visible");
}
});
}
if (ygridlines) {
ygridlines
.selectAll("path")
.forEach(function (element, i) {
if (element.attribute("gadfly:inscale") == "true") {
var bbox = element.node.getBBox();
if (bounds.y1 - bbox.y < pan_bounds.y0) {
pan_bounds.y0 = bounds.y1 - bbox.y;
}
if (bounds.y0 - bbox.y > pan_bounds.y1) {
pan_bounds.y1 = bounds.y0 - bbox.y;
}
element.attr("visibility", "visible");
}
});
}
// nudge these values a little
pan_bounds.x0 -= 5;
pan_bounds.x1 += 5;
pan_bounds.y0 -= 5;
pan_bounds.y1 += 5;
root.data("pan_bounds", pan_bounds);
root.data("zoompan-ready", true)
};
// Panning
Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {
var root = this.plotroot();
var px_per_mm = root.data("px_per_mm");
dx /= px_per_mm;
dy /= px_per_mm;
var tx0 = root.data("tx"),
ty0 = root.data("ty");
var dx0 = root.data("dx"),
dy0 = root.data("dy");
root.data("dx", dx);
root.data("dy", dy);
dx = dx - dx0;
dy = dy - dy0;
var tx = tx0 + dx,
ty = ty0 + dy;
set_plot_pan_zoom(root, tx, ty, root.data("scale"));
};
Gadfly.guide_background_drag_onstart = function(x, y, event) {
var root = this.plotroot();
root.data("dx", 0);
root.data("dy", 0);
init_pan_zoom(root);
};
Gadfly.guide_background_drag_onend = function(event) {
var root = this.plotroot();
};
Gadfly.guide_background_scroll = function(event) {
if (event.shiftKey) {
var root = this.plotroot();
init_pan_zoom(root);
var new_scale = root.data("scale") * Math.pow(2, 0.002 * event.wheelDelta);
new_scale = Math.max(
root.data("min_scale"),
Math.min(root.data("max_scale"), new_scale))
update_plot_scale(root, new_scale);
event.stopPropagation();
}
};
Gadfly.zoomslider_button_mouseover = function(event) {
this.select(".button_logo")
.animate({fill: this.data("mouseover_color")}, 100);
};
Gadfly.zoomslider_button_mouseout = function(event) {
this.select(".button_logo")
.animate({fill: this.data("mouseout_color")}, 100);
};
Gadfly.zoomslider_zoomout_click = function(event) {
var root = this.plotroot();
init_pan_zoom(root);
var min_scale = root.data("min_scale"),
scale = root.data("scale");
Snap.animate(
scale,
Math.max(min_scale, scale / 1.5),
function (new_scale) {
update_plot_scale(root, new_scale);
},
200);
};
Gadfly.zoomslider_zoomin_click = function(event) {
var root = this.plotroot();
init_pan_zoom(root);
var max_scale = root.data("max_scale"),
scale = root.data("scale");
Snap.animate(
scale,
Math.min(max_scale, scale * 1.5),
function (new_scale) {
update_plot_scale(root, new_scale);
},
200);
};
Gadfly.zoomslider_track_click = function(event) {
// TODO
};
Gadfly.zoomslider_thumb_mousedown = function(event) {
this.animate({fill: this.data("mouseover_color")}, 100);
};
Gadfly.zoomslider_thumb_mouseup = function(event) {
this.animate({fill: this.data("mouseout_color")}, 100);
};
// compute the position in [0, 1] of the zoom slider thumb from the current scale
var slider_position_from_scale = function(scale, min_scale, max_scale) {
if (scale >= 1.0) {
return 0.5 + 0.5 * (Math.log(scale) / Math.log(max_scale));
}
else {
return 0.5 * (Math.log(scale) - Math.log(min_scale)) / (0 - Math.log(min_scale));
}
}
var update_plot_scale = function(root, new_scale) {
var trans = scale_centered_translation(root, new_scale);
set_plot_pan_zoom(root, trans.x, trans.y, new_scale);
root.selectAll(".zoomslider_thumb")
.forEach(function (element, i) {
var min_pos = element.data("min_pos"),
max_pos = element.data("max_pos"),
min_scale = root.data("min_scale"),
max_scale = root.data("max_scale");
var xmid = (min_pos + max_pos) / 2;
var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);
element.transform(new Snap.Matrix().translate(
Math.max(min_pos, Math.min(
max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));
});
};
Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y) {
var root = this.plotroot();
var min_pos = this.data("min_pos"),
max_pos = this.data("max_pos"),
min_scale = root.data("min_scale"),
max_scale = root.data("max_scale"),
old_scale = root.data("old_scale");
var px_per_mm = root.data("px_per_mm");
dx /= px_per_mm;
dy /= px_per_mm;
var xmid = (min_pos + max_pos) / 2;
var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +
dx / (max_pos - min_pos);
// compute the new scale
var new_scale;
if (xpos >= 0.5) {
new_scale = Math.exp(2.0 * (xpos - 0.5) * Math.log(max_scale));
}
else {
new_scale = Math.exp(2.0 * xpos * (0 - Math.log(min_scale)) +
Math.log(min_scale));
}
new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));
update_plot_scale(root, new_scale);
};
Gadfly.zoomslider_thumb_dragstart = function(event) {
var root = this.plotroot();
init_pan_zoom(root);
// keep track of what the scale was when we started dragging
root.data("old_scale", root.data("scale"));
};
Gadfly.zoomslider_thumb_dragend = function(event) {
};
var toggle_color_class = function(root, color_class, ison) {
var guides = root.selectAll(".guide." + color_class + ",.guide ." + color_class);
var geoms = root.selectAll(".geometry." + color_class + ",.geometry ." + color_class);
if (ison) {
guides.animate({opacity: 0.5}, 250);
geoms.animate({opacity: 0.0}, 250);
} else {
guides.animate({opacity: 1.0}, 250);
geoms.animate({opacity: 1.0}, 250);
}
};
Gadfly.colorkey_swatch_click = function(event) {
var root = this.plotroot();
var color_class = this.data("color_class");
if (event.shiftKey) {
root.selectAll(".colorkey text")
.forEach(function (element) {
var other_color_class = element.data("color_class");
if (other_color_class != color_class) {
toggle_color_class(root, other_color_class,
element.attr("opacity") == 1.0);
}
});
} else {
toggle_color_class(root, color_class, this.attr("opacity") == 1.0);
}
};
return Gadfly;
}));
//@ sourceURL=gadfly.js
(function (glob, factory) {
// AMD support
if (typeof require === "function" && typeof define === "function" && define.amd) {
require(["Snap.svg", "Gadfly"], function (Snap, Gadfly) {
factory(Snap, Gadfly);
});
} else {
factory(glob.Snap, glob.Gadfly);
}
})(window, function (Snap, Gadfly) {
var fig = Snap("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe");
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-4")
.mouseenter(Gadfly.plot_mouseover)
.mouseleave(Gadfly.plot_mouseout)
.mousewheel(Gadfly.guide_background_scroll)
.drag(Gadfly.guide_background_drag_onmove,
Gadfly.guide_background_drag_onstart,
Gadfly.guide_background_drag_onend)
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-7")
.plotroot().data("unfocused_ygrid_color", "#D0D0E0")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-7")
.plotroot().data("focused_ygrid_color", "#A0A0A0")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-8")
.plotroot().data("unfocused_xgrid_color", "#D0D0E0")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-8")
.plotroot().data("focused_xgrid_color", "#A0A0A0")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-12")
.data("mouseover_color", "#cd5c5c")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-12")
.data("mouseout_color", "#6a6a6a")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-12")
.click(Gadfly.zoomslider_zoomin_click)
.mouseenter(Gadfly.zoomslider_button_mouseover)
.mouseleave(Gadfly.zoomslider_button_mouseout)
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-14")
.data("max_pos", 279)
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-14")
.data("min_pos", 262)
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-14")
.click(Gadfly.zoomslider_track_click);
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-15")
.data("max_pos", 279)
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-15")
.data("min_pos", 262)
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-15")
.data("mouseover_color", "#cd5c5c")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-15")
.data("mouseout_color", "#6a6a6a")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-15")
.drag(Gadfly.zoomslider_thumb_dragmove,
Gadfly.zoomslider_thumb_dragstart,
Gadfly.zoomslider_thumb_dragend)
.mousedown(Gadfly.zoomslider_thumb_mousedown)
.mouseup(Gadfly.zoomslider_thumb_mouseup)
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-16")
.data("mouseover_color", "#cd5c5c")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-16")
.data("mouseout_color", "#6a6a6a")
;
fig.select("#fig-e2dac0c6a0ef4ce3a5e31a77a521cdfe-element-16")
.click(Gadfly.zoomslider_zoomout_click)
.mouseenter(Gadfly.zoomslider_button_mouseover)
.mouseleave(Gadfly.zoomslider_button_mouseout)
;
});
]]> </script>
</svg>
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