<snapdata remixID="13525251"><project name="bezier curves" app="Snap! 10, https://snap.berkeley.edu" version="2"><notes>drag the points around on the stage!</notes><thumbnail>data:image/png;base64,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</thumbnail><scenes select="1"><scene name="bezier curves"><notes>drag the points around on the stage!</notes><hidden></hidden><headers></headers><code></code><blocks><block-definition s="draw quadratic bezier: p0 %&apos;p0&apos; p1 %&apos;p1&apos; p2 %&apos;p2&apos; in %&apos;n&apos; steps" type="command" category="pen"><header></header><code></code><translations></translations><inputs><input type="%l" initial="2" min="2" max="2"></input><input type="%l" initial="1"></input><input type="%l" initial="1"></input><input type="%n" initial="1"></input></inputs><script><block s="doWarp"><script><block s="doGotoObject"><custom-block s="point at t = %n on quadratic bezier: p0 %n p1 %n p2 %n"><l>0</l><block var="p0"/><block var="p1"/><block var="p2"/></custom-block></block><block s="down"></block><block s="doFor"><l>tn</l><l>1</l><block var="n"/><script><block s="doGotoObject"><custom-block s="point at t = %n on quadratic bezier: p0 %n p1 %n p2 %n"><block s="reportQuotient"><block var="tn"/><block var="n"/></block><block var="p0"/><block var="p1"/><block var="p2"/></custom-block></block></script></block><block s="up"></block></script></block></script></block-definition><block-definition s="point at t = %&apos;t&apos; on quadratic bezier: p0 %&apos;p0&apos; p1 %&apos;p1&apos; p2 %&apos;p2&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n" initial="1"></input><input type="%n" initial="1"></input><input type="%n" initial="1"></input><input type="%n" initial="1"></input></inputs><script><block s="doReport"><block s="reportVariadicSum"><list><block s="reportVariadicProduct"><list><block s="reportPower"><block s="reportDifference"><l>1</l><block var="t"/></block><l>2</l></block><block var="p0"/></list></block><block s="reportVariadicProduct"><list><l>2</l><block s="reportDifference"><l>1</l><block var="t"/></block><block var="t"/><block var="p1"/></list></block><block s="reportVariadicProduct"><list><block s="reportPower"><block var="t"/><l>2</l></block><block var="p2"/></list></block></list></block></block></script></block-definition></blocks><primitives></primitives><stage name="Stage" width="480" height="360" costume="0" color="255,255,255,1" tempo="60" threadsafe="false" penlog="false" volume="100" pan="0" lines="round" ternary="false" hyperops="true" codify="false" inheritance="true" sublistIDs="false" 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</pentrails><costumes><list 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